diff --git a/src/Storages/MergeTree/MergeTask.cpp b/src/Storages/MergeTree/MergeTask.cpp
index 5b8df976d475..1c543f2f5491 100644
--- a/src/Storages/MergeTree/MergeTask.cpp
+++ b/src/Storages/MergeTree/MergeTask.cpp
@@ -532,9 +532,7 @@ bool MergeTask::ExecuteAndFinalizeHorizontalPart::prepare() const
         !patch_parts.empty() ||
         global_ctx->cleanup ||
         global_ctx->deduplicate ||
-        global_ctx->merging_params.mode == MergeTreeData::MergingParams::Collapsing ||
-        global_ctx->merging_params.mode == MergeTreeData::MergingParams::Replacing ||
-        global_ctx->merging_params.mode == MergeTreeData::MergingParams::VersionedCollapsing;
+        global_ctx->merging_params.mode != MergeTreeData::MergingParams::Ordinary;
 
     prepareProjectionsToMergeAndRebuild();
 
diff --git a/tests/queries/0_stateless/03786_projection_part_offset_reducing_merge.reference b/tests/queries/0_stateless/03786_projection_part_offset_reducing_merge.reference
new file mode 100644
index 000000000000..5d778a7b1b43
--- /dev/null
+++ b/tests/queries/0_stateless/03786_projection_part_offset_reducing_merge.reference
@@ -0,0 +1,3 @@
+coalescing	1
+summing	1
+aggregating	1
diff --git a/tests/queries/0_stateless/03786_projection_part_offset_reducing_merge.sql b/tests/queries/0_stateless/03786_projection_part_offset_reducing_merge.sql
new file mode 100644
index 000000000000..0c88a200237c
--- /dev/null
+++ b/tests/queries/0_stateless/03786_projection_part_offset_reducing_merge.sql
@@ -0,0 +1,67 @@
+-- Regression test for a crash (Logical error: 'page_pos < pages.size()') that happened when
+-- OPTIMIZE-ing a table whose engine combines rows (Coalescing/Summing/Aggregating/...) and that
+-- has a projection carrying the parent _part_offset.
+--
+-- Such merges reduce rows, so the source-to-merged offset mapping is incomplete and the projection
+-- must be rebuilt rather than merged. Before the fix these engines were missing from
+-- merge_may_reduce_rows, so the projection was merged and the offset remap read out of bounds.
+--
+-- The self-join below checks that every rebuilt projection row points back to the base row with the
+-- same key, i.e. its stored _parent_part_offset equals the base _part_offset.
+
+DROP TABLE IF EXISTS t_coalescing;
+CREATE TABLE t_coalescing
+(
+    a Int32,
+    v Nullable(Int64),
+    PROJECTION p (SELECT a, _part_offset ORDER BY a)
+)
+ENGINE = CoalescingMergeTree
+ORDER BY a
+SETTINGS deduplicate_merge_projection_mode = 'rebuild';
+
+INSERT INTO t_coalescing SELECT number, number FROM numbers(1000);
+INSERT INTO t_coalescing SELECT number, NULL FROM numbers(1000);
+OPTIMIZE TABLE t_coalescing FINAL;
+SELECT 'coalescing', count() = sum(l._part_offset = r._parent_part_offset)
+FROM t_coalescing l JOIN mergeTreeProjection(currentDatabase(), t_coalescing, p) r USING (a)
+SETTINGS enable_analyzer = 1;
+DROP TABLE t_coalescing;
+
+DROP TABLE IF EXISTS t_summing;
+CREATE TABLE t_summing
+(
+    a Int32,
+    v Int64,
+    PROJECTION p (SELECT a, _part_offset ORDER BY a)
+)
+ENGINE = SummingMergeTree
+ORDER BY a
+SETTINGS deduplicate_merge_projection_mode = 'rebuild';
+
+INSERT INTO t_summing SELECT number, 1 FROM numbers(1000);
+INSERT INTO t_summing SELECT number, 10 FROM numbers(1000);
+OPTIMIZE TABLE t_summing FINAL;
+SELECT 'summing', count() = sum(l._part_offset = r._parent_part_offset)
+FROM t_summing l JOIN mergeTreeProjection(currentDatabase(), t_summing, p) r USING (a)
+SETTINGS enable_analyzer = 1;
+DROP TABLE t_summing;
+
+DROP TABLE IF EXISTS t_aggregating;
+CREATE TABLE t_aggregating
+(
+    a Int32,
+    v SimpleAggregateFunction(sum, Int64),
+    PROJECTION p (SELECT a, _part_offset ORDER BY a)
+)
+ENGINE = AggregatingMergeTree
+ORDER BY a
+SETTINGS deduplicate_merge_projection_mode = 'rebuild';
+
+INSERT INTO t_aggregating SELECT number, 1 FROM numbers(1000);
+INSERT INTO t_aggregating SELECT number, 10 FROM numbers(1000);
+OPTIMIZE TABLE t_aggregating FINAL;
+SELECT 'aggregating', count() = sum(l._part_offset = r._parent_part_offset)
+FROM t_aggregating l JOIN mergeTreeProjection(currentDatabase(), t_aggregating, p) r USING (a)
+SETTINGS enable_analyzer = 1;
+DROP TABLE t_aggregating;