diff --git a/bigframes/core/blocks.py b/bigframes/core/blocks.py
index 2a888125f8..5965c96374 100644
--- a/bigframes/core/blocks.py
+++ b/bigframes/core/blocks.py
@@ -27,7 +27,7 @@
 import os
 import random
 import typing
-from typing import Iterable, List, Literal, Mapping, Optional, Sequence, Tuple
+from typing import Iterable, List, Literal, Mapping, Optional, Sequence, Tuple, Union
 import warnings
 
 import google.cloud.bigquery as bigquery
@@ -105,6 +105,8 @@ def __init__(
         index_columns: Iterable[str],
         column_labels: typing.Union[pd.Index, typing.Iterable[Label]],
         index_labels: typing.Union[pd.Index, typing.Iterable[Label], None] = None,
+        *,
+        transpose_cache: Optional[Block] = None,
     ):
         """Construct a block object, will create default index if no index columns specified."""
         index_columns = list(index_columns)
@@ -144,6 +146,7 @@ def __init__(
         # TODO(kemppeterson) Add a cache for corr to parallel the single-column stats.
 
         self._stats_cache[" ".join(self.index_columns)] = {}
+        self._transpose_cache: Optional[Block] = transpose_cache
 
     @classmethod
     def from_local(cls, data: pd.DataFrame, session: bigframes.Session) -> Block:
@@ -716,6 +719,15 @@ def with_column_labels(
             index_labels=self.index.names,
         )
 
+    def with_transpose_cache(self, transposed: Block):
+        return Block(
+            self._expr,
+            index_columns=self.index_columns,
+            column_labels=self._column_labels,
+            index_labels=self.index.names,
+            transpose_cache=transposed,
+        )
+
     def with_index_labels(self, value: typing.Sequence[Label]) -> Block:
         if len(value) != len(self.index_columns):
             raise ValueError(
@@ -804,18 +816,35 @@ def multi_apply_window_op(
     def multi_apply_unary_op(
         self,
         columns: typing.Sequence[str],
-        op: ops.UnaryOp,
+        op: Union[ops.UnaryOp, ex.Expression],
     ) -> Block:
+        if isinstance(op, ops.UnaryOp):
+            input_varname = guid.generate_guid()
+            expr = op.as_expr(input_varname)
+        else:
+            input_varnames = op.unbound_variables
+            assert len(input_varnames) == 1
+            expr = op
+            input_varname = input_varnames[0]
+
         block = self
-        for i, col_id in enumerate(columns):
+        for col_id in columns:
             label = self.col_id_to_label[col_id]
-            block, result_id = block.apply_unary_op(
-                col_id,
-                op,
-                result_label=label,
+            block, result_id = block.project_expr(
+                expr.bind_all_variables({input_varname: ex.free_var(col_id)}),
+                label=label,
             )
             block = block.copy_values(result_id, col_id)
             block = block.drop_columns([result_id])
+        # Special case, we can preserve transpose cache for full-frame unary ops
+        if (self._transpose_cache is not None) and set(self.value_columns) == set(
+            columns
+        ):
+            transpose_columns = self._transpose_cache.value_columns
+            new_transpose_cache = self._transpose_cache.multi_apply_unary_op(
+                transpose_columns, op
+            )
+            block = block.with_transpose_cache(new_transpose_cache)
         return block
 
     def apply_window_op(
@@ -922,20 +951,17 @@ def aggregate_all_and_stack(
                 (ex.UnaryAggregation(operation, ex.free_var(col_id)), col_id)
                 for col_id in self.value_columns
             ]
-            index_col_ids = [
-                guid.generate_guid() for i in range(self.column_labels.nlevels)
-            ]
-            result_expr = self.expr.aggregate(aggregations, dropna=dropna).unpivot(
-                row_labels=self.column_labels.to_list(),
-                index_col_ids=index_col_ids,
-                unpivot_columns=tuple([(value_col_id, tuple(self.value_columns))]),
-            )
+            index_id = guid.generate_guid()
+            result_expr = self.expr.aggregate(
+                aggregations, dropna=dropna
+            ).assign_constant(index_id, None, None)
+            # Transpose as last operation so that final block has valid transpose cache
             return Block(
                 result_expr,
-                index_columns=index_col_ids,
-                column_labels=[None],
-                index_labels=self.column_labels.names,
-            )
+                index_columns=[index_id],
+                column_labels=self.column_labels,
+                index_labels=[None],
+            ).transpose(original_row_index=pd.Index([None]))
         else:  # axis_n == 1
             # using offsets as identity to group on.
             # TODO: Allow to promote identity/total_order columns instead for better perf
@@ -1575,10 +1601,19 @@ def melt(
             index_columns=[index_id],
         )
 
-    def transpose(self) -> Block:
-        """Transpose the block. Will fail if dtypes aren't coercible to a common type or too many rows"""
+    def transpose(self, *, original_row_index: Optional[pd.Index] = None) -> Block:
+        """Transpose the block. Will fail if dtypes aren't coercible to a common type or too many rows.
+        Can provide the original_row_index directly if it is already known, otherwise a query is needed.
+        """
+        if self._transpose_cache is not None:
+            return self._transpose_cache.with_transpose_cache(self)
+
         original_col_index = self.column_labels
-        original_row_index = self.index.to_pandas()
+        original_row_index = (
+            original_row_index
+            if original_row_index is not None
+            else self.index.to_pandas()
+        )
         original_row_count = len(original_row_index)
         if original_row_count > bigframes.constants.MAX_COLUMNS:
             raise NotImplementedError(
@@ -1619,6 +1654,7 @@ def transpose(self) -> Block:
             result.with_column_labels(original_row_index)
             .order_by([ordering.ascending_over(result.index_columns[-1])])
             .drop_levels([result.index_columns[-1]])
+            .with_transpose_cache(self)
         )
 
     def _create_stack_column(
diff --git a/bigframes/core/compile/compiled.py b/bigframes/core/compile/compiled.py
index a59d599679..88c1006c79 100644
--- a/bigframes/core/compile/compiled.py
+++ b/bigframes/core/compile/compiled.py
@@ -823,17 +823,14 @@ def to_sql(
                 for col in baked_ir.column_ids
             ]
             selection = ", ".join(map(lambda col_id: f"`{col_id}`", output_columns))
-            order_by_clause = baked_ir._ordering_clause(
-                baked_ir._ordering.all_ordering_columns
-            )
 
-            sql = textwrap.dedent(
-                f"SELECT {selection}\n"
-                "FROM (\n"
-                f"{sql}\n"
-                ")\n"
-                f"{order_by_clause}\n"
-            )
+            sql = textwrap.dedent(f"SELECT {selection}\n" "FROM (\n" f"{sql}\n" ")\n")
+            # Single row frames may not have any ordering columns
+            if len(baked_ir._ordering.all_ordering_columns) > 0:
+                order_by_clause = baked_ir._ordering_clause(
+                    baked_ir._ordering.all_ordering_columns
+                )
+                sql += f"{order_by_clause}\n"
         else:
             sql = ibis_bigquery.Backend().compile(
                 self._to_ibis_expr(
diff --git a/bigframes/core/ordering.py b/bigframes/core/ordering.py
index 2543a3b722..9009e31be3 100644
--- a/bigframes/core/ordering.py
+++ b/bigframes/core/ordering.py
@@ -167,6 +167,8 @@ def _truncate_ordering(
                 truncated_refs.append(order_part)
                 if columns_seen.issuperset(must_see):
                     return tuple(truncated_refs)
+        if len(must_see) == 0:
+            return ()
         raise ValueError("Ordering did not contain all total_order_cols")
 
     def with_reverse(self):
diff --git a/bigframes/dataframe.py b/bigframes/dataframe.py
index a55b7f569b..48c4af7a37 100644
--- a/bigframes/dataframe.py
+++ b/bigframes/dataframe.py
@@ -693,18 +693,19 @@ def _apply_binop(
     def _apply_scalar_binop(
         self, other: float | int, op: ops.BinaryOp, reverse: bool = False
     ) -> DataFrame:
-        block = self._block
-        for column_id, label in zip(
-            self._block.value_columns, self._block.column_labels
-        ):
-            expr = (
-                op.as_expr(ex.const(other), column_id)
-                if reverse
-                else op.as_expr(column_id, ex.const(other))
+        if reverse:
+            expr = op.as_expr(
+                left_input=ex.const(other),
+                right_input=bigframes.core.guid.generate_guid(),
             )
-            block, _ = block.project_expr(expr, label)
-            block = block.drop_columns([column_id])
-        return DataFrame(block)
+        else:
+            expr = op.as_expr(
+                left_input=bigframes.core.guid.generate_guid(),
+                right_input=ex.const(other),
+            )
+        return DataFrame(
+            self._block.multi_apply_unary_op(self._block.value_columns, expr)
+        )
 
     def _apply_series_binop_axis_0(
         self,
@@ -1974,7 +1975,7 @@ def any(
         else:
             frame = self._drop_non_bool()
         block = frame._block.aggregate_all_and_stack(agg_ops.any_op, axis=axis)
-        return bigframes.series.Series(block.select_column("values"))
+        return bigframes.series.Series(block)
 
     def all(
         self, axis: typing.Union[str, int] = 0, *, bool_only: bool = False
@@ -1984,7 +1985,7 @@ def all(
         else:
             frame = self._drop_non_bool()
         block = frame._block.aggregate_all_and_stack(agg_ops.all_op, axis=axis)
-        return bigframes.series.Series(block.select_column("values"))
+        return bigframes.series.Series(block)
 
     def sum(
         self, axis: typing.Union[str, int] = 0, *, numeric_only: bool = False
@@ -1994,7 +1995,7 @@ def sum(
         else:
             frame = self._drop_non_numeric()
         block = frame._block.aggregate_all_and_stack(agg_ops.sum_op, axis=axis)
-        return bigframes.series.Series(block.select_column("values"))
+        return bigframes.series.Series(block)
 
     def mean(
         self, axis: typing.Union[str, int] = 0, *, numeric_only: bool = False
@@ -2004,7 +2005,7 @@ def mean(
         else:
             frame = self._drop_non_numeric()
         block = frame._block.aggregate_all_and_stack(agg_ops.mean_op, axis=axis)
-        return bigframes.series.Series(block.select_column("values"))
+        return bigframes.series.Series(block)
 
     def median(
         self, *, numeric_only: bool = False, exact: bool = True
@@ -2019,7 +2020,7 @@ def median(
             return result
         else:
             block = frame._block.aggregate_all_and_stack(agg_ops.median_op)
-            return bigframes.series.Series(block.select_column("values"))
+            return bigframes.series.Series(block)
 
     def quantile(
         self, q: Union[float, Sequence[float]] = 0.5, *, numeric_only: bool = False
@@ -2052,7 +2053,7 @@ def std(
         else:
             frame = self._drop_non_numeric()
         block = frame._block.aggregate_all_and_stack(agg_ops.std_op, axis=axis)
-        return bigframes.series.Series(block.select_column("values"))
+        return bigframes.series.Series(block)
 
     def var(
         self, axis: typing.Union[str, int] = 0, *, numeric_only: bool = False
@@ -2062,7 +2063,7 @@ def var(
         else:
             frame = self._drop_non_numeric()
         block = frame._block.aggregate_all_and_stack(agg_ops.var_op, axis=axis)
-        return bigframes.series.Series(block.select_column("values"))
+        return bigframes.series.Series(block)
 
     def min(
         self, axis: typing.Union[str, int] = 0, *, numeric_only: bool = False
@@ -2072,7 +2073,7 @@ def min(
         else:
             frame = self._drop_non_numeric()
         block = frame._block.aggregate_all_and_stack(agg_ops.min_op, axis=axis)
-        return bigframes.series.Series(block.select_column("values"))
+        return bigframes.series.Series(block)
 
     def max(
         self, axis: typing.Union[str, int] = 0, *, numeric_only: bool = False
@@ -2082,7 +2083,7 @@ def max(
         else:
             frame = self._drop_non_numeric()
         block = frame._block.aggregate_all_and_stack(agg_ops.max_op, axis=axis)
-        return bigframes.series.Series(block.select_column("values"))
+        return bigframes.series.Series(block)
 
     def prod(
         self, axis: typing.Union[str, int] = 0, *, numeric_only: bool = False
@@ -2092,7 +2093,7 @@ def prod(
         else:
             frame = self._drop_non_numeric()
         block = frame._block.aggregate_all_and_stack(agg_ops.product_op, axis=axis)
-        return bigframes.series.Series(block.select_column("values"))
+        return bigframes.series.Series(block)
 
     product = prod
     product.__doc__ = inspect.getdoc(vendored_pandas_frame.DataFrame.prod)
@@ -2103,11 +2104,11 @@ def count(self, *, numeric_only: bool = False) -> bigframes.series.Series:
         else:
             frame = self._drop_non_numeric()
         block = frame._block.aggregate_all_and_stack(agg_ops.count_op)
-        return bigframes.series.Series(block.select_column("values"))
+        return bigframes.series.Series(block)
 
     def nunique(self) -> bigframes.series.Series:
         block = self._block.aggregate_all_and_stack(agg_ops.nunique_op)
-        return bigframes.series.Series(block.select_column("values"))
+        return bigframes.series.Series(block)
 
     def agg(
         self, func: str | typing.Sequence[str]
diff --git a/tests/system/small/test_dataframe.py b/tests/system/small/test_dataframe.py
index f41a21add0..d33cb7d148 100644
--- a/tests/system/small/test_dataframe.py
+++ b/tests/system/small/test_dataframe.py
@@ -2488,6 +2488,20 @@ def test_df_transpose_error():
         dataframe.DataFrame([[1, "hello"], [2, "world"]]).transpose()
 
 
+def test_df_transpose_repeated_uses_cache():
+    bf_df = dataframe.DataFrame([[1, 2.5], [2, 3.5]])
+    pd_df = pandas.DataFrame([[1, 2.5], [2, 3.5]])
+    # Transposing many times so that operation will fail from complexity if not using cache
+    for i in range(10):
+        # Cache still works even with simple scalar binop
+        bf_df = bf_df.transpose() + i
+        pd_df = pd_df.transpose() + i
+
+    pd.testing.assert_frame_equal(
+        pd_df, bf_df.to_pandas(), check_dtype=False, check_index_type=False
+    )
+
+
 @pytest.mark.parametrize(
     ("ordered"),
     [