diff --git a/spring-data-jpa/src/main/antlr4/org/springframework/data/jpa/repository/query/Jpql.g4 b/spring-data-jpa/src/main/antlr4/org/springframework/data/jpa/repository/query/Jpql.g4
index e0e2a0a35..24e18e1cb 100644
--- a/spring-data-jpa/src/main/antlr4/org/springframework/data/jpa/repository/query/Jpql.g4
+++ b/spring-data-jpa/src/main/antlr4/org/springframework/data/jpa/repository/query/Jpql.g4
@@ -43,7 +43,13 @@ ql_statement
     ;
 
 select_statement
-    : select_clause from_clause (where_clause)? (groupby_clause)? (having_clause)? (orderby_clause)?
+    : select_clause from_clause (where_clause)? (groupby_clause)? (having_clause)? (orderby_clause)? (setOperator_with_select_statement)*
+    ;
+
+setOperator_with_select_statement
+    : INTERSECT select_statement
+    | UNION select_statement
+    | EXCEPT select_statement
     ;
 
 update_statement
@@ -443,6 +449,7 @@ string_expression
     | aggregate_expression
     | case_expression
     | function_invocation
+    | string_expression op='||' string_expression
     | string_cast_function
     | type_cast_function
     | '(' subquery ')'
@@ -908,6 +915,7 @@ ELSE                        : E L S E;
 EMPTY                       : E M P T Y;
 ENTRY                       : E N T R Y;
 ESCAPE                      : E S C A P E;
+EXCEPT                      : E X C E P T;
 EXISTS                      : E X I S T S;
 EXP                         : E X P;
 EXTRACT                     : E X T R A C T;
@@ -972,6 +980,7 @@ TREAT                       : T R E A T;
 TRIM                        : T R I M;
 TRUE                        : T R U E;
 TYPE                        : T Y P E;
+UNION                       : U N I O N;
 UPDATE                      : U P D A T E;
 UPPER                       : U P P E R;
 VALUE                       : V A L U E;
diff --git a/spring-data-jpa/src/main/java/org/springframework/data/jpa/repository/query/JpqlQueryRenderer.java b/spring-data-jpa/src/main/java/org/springframework/data/jpa/repository/query/JpqlQueryRenderer.java
index 41ca18396..37295be4f 100644
--- a/spring-data-jpa/src/main/java/org/springframework/data/jpa/repository/query/JpqlQueryRenderer.java
+++ b/spring-data-jpa/src/main/java/org/springframework/data/jpa/repository/query/JpqlQueryRenderer.java
@@ -80,6 +80,29 @@ class JpqlQueryRenderer extends JpqlBaseVisitor<QueryTokenStream> {
 			builder.appendExpression(visit(ctx.orderby_clause()));
 		}
 
+		ctx.setOperator_with_select_statement().forEach(setOperatorWithSelectStatementContext -> {
+			tokens.addAll(visit(setOperatorWithSelectStatementContext));
+		});
+
+		return tokens;
+	}
+
+	@Override
+	public List<JpaQueryParsingToken> visitSetOperator_with_select_statement(
+			JpqlParser.SetOperator_with_select_statementContext ctx) {
+
+		List<JpaQueryParsingToken> tokens = new ArrayList<>();
+
+		if (ctx.INTERSECT() != null) {
+			tokens.add(new JpaQueryParsingToken(ctx.INTERSECT()));
+		} else if (ctx.UNION() != null) {
+			tokens.add(new JpaQueryParsingToken(ctx.UNION()));
+		} else if (ctx.EXCEPT() != null) {
+			tokens.add(new JpaQueryParsingToken(ctx.EXCEPT()));
+		}
+
+		tokens.addAll(visit(ctx.select_statement()));
+
 		return builder;
 	}
 
@@ -800,6 +823,25 @@ class JpqlQueryRenderer extends JpqlBaseVisitor<QueryTokenStream> {
 		if (ctx.nullsPrecedence() != null) {
 			builder.append(visit(ctx.nullsPrecedence()));
 		}
+		if (ctx.nullsPrecedence() != null) {
+			tokens.addAll(visit(ctx.nullsPrecedence()));
+		}
+
+		return tokens;
+	}
+
+	@Override
+	public List<JpaQueryParsingToken> visitNullsPrecedence(JpqlParser.NullsPrecedenceContext ctx) {
+
+		List<JpaQueryParsingToken> tokens = new ArrayList<>();
+
+		tokens.add(new JpaQueryParsingToken(ctx.NULLS()));
+
+		if (ctx.FIRST() != null) {
+			tokens.add(new JpaQueryParsingToken(ctx.FIRST()));
+		} else if (ctx.LAST() != null) {
+			tokens.add(new JpaQueryParsingToken(ctx.LAST()));
+		}
 
 		return builder;
 	}
@@ -1518,6 +1560,11 @@ class JpqlQueryRenderer extends JpqlBaseVisitor<QueryTokenStream> {
 			builder.append(visit(ctx.type_cast_function()));
 		} else if (ctx.function_invocation() != null) {
 			builder.append(visit(ctx.function_invocation()));
+		} else if (ctx.op != null) {
+
+			tokens.addAll(visit(ctx.string_expression(0)));
+			tokens.add(new JpaQueryParsingToken(ctx.op));
+			tokens.addAll(visit(ctx.string_expression(1)));
 		} else if (ctx.subquery() != null) {
 
 			builder.append(TOKEN_OPEN_PAREN);
diff --git a/spring-data-jpa/src/test/java/org/springframework/data/jpa/repository/query/HqlQueryRendererTests.java b/spring-data-jpa/src/test/java/org/springframework/data/jpa/repository/query/HqlQueryRendererTests.java
index 6abc8b504..8102c99cc 100644
--- a/spring-data-jpa/src/test/java/org/springframework/data/jpa/repository/query/HqlQueryRendererTests.java
+++ b/spring-data-jpa/src/test/java/org/springframework/data/jpa/repository/query/HqlQueryRendererTests.java
@@ -1651,29 +1651,25 @@ class HqlQueryRendererTests {
 	@Test // GH-2962
 	void orderByWithNullsFirstOrLastShouldWork() {
 
-		assertThatNoException().isThrownBy(() -> {
-			parseWithoutChanges("""
-					select a,
-						case
-							when a.geaendertAm is null then a.erstelltAm
-							else a.geaendertAm end as mutationAm
-					from Element a
-					where a.erstelltDurch = :variable
-					order by mutationAm desc nulls first
-					""");
-		});
+		assertQuery("""
+				select a,
+					case
+						when a.geaendertAm is null then a.erstelltAm
+						else a.geaendertAm end as mutationAm
+				from Element a
+				where a.erstelltDurch = :variable
+				order by mutationAm desc nulls first
+				""");
 
-		assertThatNoException().isThrownBy(() -> {
-			parseWithoutChanges("""
-						select a,
-							case
-								when a.geaendertAm is null then a.erstelltAm
-								else a.geaendertAm end as mutationAm
-						from Element a
-						where a.erstelltDurch = :variable
-						order by mutationAm desc nulls last
+		assertQuery("""
+				select a,
+					case
+						when a.geaendertAm is null then a.erstelltAm
+						else a.geaendertAm end as mutationAm
+				from Element a
+				where a.erstelltDurch = :variable
+				order by mutationAm desc nulls last
 					""");
-		});
 	}
 
 	@Test // GH-3882
@@ -1693,14 +1689,12 @@ class HqlQueryRendererTests {
 	@Test // GH-2964
 	void roundFunctionShouldWorkLikeAnyOtherFunction() {
 
-		assertThatNoException().isThrownBy(() -> {
-			parseWithoutChanges("""
-					select round(count(ri) * 100 / max(ri.receipt.positions), 0) as perc
-					from StockOrderItem oi
-					right join StockReceiptItem ri
-					on ri.article = oi.article
-					""");
-		});
+		assertQuery("""
+				select round(count(ri)*100/max(ri.receipt.positions), 0) as perc
+				from StockOrderItem oi
+				right join StockReceiptItem ri
+				on ri.article = oi.article
+				""");
 	}
 
 	@Test // GH-3711
@@ -1883,6 +1877,42 @@ class HqlQueryRendererTests {
 		assertQuery("select e.power.id from MyEntity e");
 	}
 
+	@Test // GH-3136
+	void doublePipeShouldBeValidAsAStringConcatOperator() {
+
+		assertQuery("""
+				select e.name || ' ' || e.title
+				from Employee e
+				""");
+	}
+
+	@Test // GH-3136
+	void additionalStringOperationsShouldWork() {
+
+		assertQuery("""
+				select
+					replace(e.name, 'Baggins', 'Proudfeet'),
+					left(e.role, 4),
+					right(e.home, 5),
+					cast(e.distance_from_home, int)
+				from Employee e
+				""");
+	}
+
+	@Test // GH-3136
+	void combinedSelectStatementsShouldWork() {
+
+		assertQuery("""
+				select e from Employee e where e.last_name = 'Baggins'
+				intersect
+				select e from Employee e where e.first_name = 'Samwise'
+				union
+				select e from Employee e where e.home = 'The Shire'
+				except
+				select e from Employee e where e.home = 'Isengard'
+				""");
+	}
+
 	@Test // GH-3219
 	void extractFunctionShouldSupportAdditionalExtensions() {
 
diff --git a/spring-data-jpa/src/test/java/org/springframework/data/jpa/repository/query/JpqlQueryRendererTests.java b/spring-data-jpa/src/test/java/org/springframework/data/jpa/repository/query/JpqlQueryRendererTests.java
index d3daa9e72..7cc49745e 100644
--- a/spring-data-jpa/src/test/java/org/springframework/data/jpa/repository/query/JpqlQueryRendererTests.java
+++ b/spring-data-jpa/src/test/java/org/springframework/data/jpa/repository/query/JpqlQueryRendererTests.java
@@ -1034,6 +1034,59 @@ class JpqlQueryRendererTests {
 		assertQuery("select e.power.id from MyEntity e");
 	}
 
+	@Test // GH-3136
+	void doublePipeShouldBeValidAsAStringConcatOperator() {
+
+		assertQuery("""
+				select e.name || ' ' || e.title
+				from Employee e
+				""");
+	}
+
+	@Test // GH-3136
+	void combinedSelectStatementsShouldWork() {
+
+		assertQuery("""
+				select e from Employee e where e.last_name = 'Baggins'
+				intersect
+				select e from Employee e where e.first_name = 'Samwise'
+				union
+				select e from Employee e where e.home = 'The Shire'
+				except
+				select e from Employee e where e.home = 'Isengard'
+				""");
+	}
+
+	@Disabled
+	@Test // GH-3136
+	void additionalStringOperationsShouldWork() {
+
+		assertQuery("""
+				select
+					replace(e.name, 'Baggins', 'Proudfeet'),
+					left(e.role, 4),
+					right(e.home, 5),
+					cast(e.distance_from_home, int)
+				from Employee e
+				""");
+	}
+
+	@Test // GH-3136
+	void orderByWithNullsFirstOrLastShouldWork() {
+
+		assertQuery("""
+				select a
+				from Element a
+				order by mutationAm desc nulls first
+				""");
+
+		assertQuery("""
+				select a
+				from Element a
+				order by mutationAm desc nulls last
+				""");
+	}
+
 	@ParameterizedTest // GH-3342
 	@ValueSource(strings = { "select 1 as value from User u", "select -1 as value from User u",
 			"select +1 as value from User u", "select +1 * -100 as value from User u",