diff --git a/sql/src/main/java/io/deephaven/sql/TypeAdapter.java b/sql/src/main/java/io/deephaven/sql/TypeAdapter.java
index da775daf69f..644bb9b1a73 100644
--- a/sql/src/main/java/io/deephaven/sql/TypeAdapter.java
+++ b/sql/src/main/java/io/deephaven/sql/TypeAdapter.java
@@ -117,13 +117,13 @@ public RelDataType visit(InstantType instantType) {
     @Override
     public RelDataType visit(ArrayType<?, ?> arrayType) {
         // SQLTODO(array-type)
-        throw new UnsupportedOperationException("SQLTODO(array-type)");
+        return typeFactory.createJavaType(SqlTodoArrayType.class);
     }
 
     @Override
     public RelDataType visit(CustomType<?> customType) {
         // SQLTODO(custom-type)
-        throw new UnsupportedOperationException("SQLTODO(custom-type)");
+        return typeFactory.createJavaType(SqlTodoCustomType.class);
     }
 
     private RelDataType create(SqlTypeName typeName) {
@@ -133,4 +133,19 @@ private RelDataType create(SqlTypeName typeName) {
     private RelDataType nullable(RelDataType relDataType) {
         return typeFactory.createTypeWithNullability(relDataType, true);
     }
+
+    // We currently need our type parsing to always succeed; right now, we implicitly inherit the user's scope, and if
+    // they happen to have a table with column of CustomType or ArrayType, we need to have that not immediately fail.
+    // Firstly, the user might not even be referencing that table / column. Secondly, the user might just be passing
+    // the column through unchanged, in which case Calcite is happy to create the plan.
+    // See https://github.com/deephaven/deephaven-core/issues/5443 for more context.
+
+    static class SqlTodoType {
+    }
+
+    static class SqlTodoArrayType extends SqlTodoType {
+    }
+
+    static class SqlTodoCustomType extends SqlTodoType {
+    }
 }
diff --git a/sql/src/test/java/io/deephaven/sql/SqlAdapterTest.java b/sql/src/test/java/io/deephaven/sql/SqlAdapterTest.java
index 752bab3a6ea..aace3947804 100644
--- a/sql/src/test/java/io/deephaven/sql/SqlAdapterTest.java
+++ b/sql/src/test/java/io/deephaven/sql/SqlAdapterTest.java
@@ -8,6 +8,8 @@
 import io.deephaven.qst.table.TableHeader;
 import io.deephaven.qst.table.TableSpec;
 import io.deephaven.qst.table.TicketTable;
+import io.deephaven.qst.type.Type;
+import org.apache.calcite.runtime.CalciteContextException;
 import org.junit.jupiter.api.Test;
 
 import java.io.IOException;
@@ -17,6 +19,7 @@
 import java.util.List;
 
 import static org.assertj.core.api.Assertions.assertThat;
+import static org.assertj.core.api.Assertions.failBecauseExceptionWasNotThrown;
 
 public class SqlAdapterTest {
 
@@ -45,6 +48,14 @@ public class SqlAdapterTest {
 
     private static final TableHeader TIME2 = TableHeader.of(ColumnHeader.ofInstant("Time2"));
 
+    interface MyCustomType {
+
+    }
+
+    private static final TableHeader CUSTOM = TableHeader.of(
+            ColumnHeader.of("Foo", Type.longType()),
+            ColumnHeader.of("Bar", Type.ofCustom(MyCustomType.class)));
+
     @Test
     void sql1() throws IOException, URISyntaxException {
         final Scope scope = scope(
@@ -270,10 +281,46 @@ void sql35() throws IOException, URISyntaxException {
         check(scope, 35);
     }
 
+    @Test
+    void sql36() throws IOException, URISyntaxException {
+        final Scope scope = scope("custom", CUSTOM);
+        check(scope, 36);
+    }
+
+    @Test
+    void sql37() throws IOException, URISyntaxException {
+        final Scope scope = scope("custom", CUSTOM);
+        check(scope, 37);
+    }
+
+    @Test
+    void sql38() throws IOException, URISyntaxException {
+        final Scope scope = scope("custom", CUSTOM);
+        check(scope, 38);
+    }
+
+    @Test
+    void sql39() throws IOException, URISyntaxException {
+        final Scope scope = scope("custom", CUSTOM);
+        checkError(scope, 39, CalciteContextException.class,
+                "Cannot apply '+' to arguments of type '<JAVATYPE(CLASS IO.DEEPHAVEN.SQL.TYPEADAPTER$SQLTODOCUSTOMTYPE)> + <INTEGER>'");
+    }
+
     private static void check(Scope scope, int index) throws IOException, URISyntaxException {
         check(scope, String.format("query-%d.sql", index), String.format("qst-%d.dot", index));
     }
 
+    private static void checkError(Scope scope, int index, Class<? extends Throwable> clazz, String messagePart)
+            throws IOException, URISyntaxException {
+        try {
+            SqlAdapter.parseSql(read(String.format("query-%d.sql", index)), scope);
+            failBecauseExceptionWasNotThrown(clazz);
+        } catch (Throwable t) {
+            assertThat(t).isInstanceOf(clazz);
+            assertThat(t).hasMessageContaining(messagePart);
+        }
+    }
+
     private static void check(Scope scope, String queryResource, String expectedResource)
             throws IOException, URISyntaxException {
         checkSql(expectedResource, read(queryResource), scope);
diff --git a/sql/src/test/resources/io/deephaven/sql/qst-36.dot b/sql/src/test/resources/io/deephaven/sql/qst-36.dot
new file mode 100644
index 00000000000..487b9b03ce5
--- /dev/null
+++ b/sql/src/test/resources/io/deephaven/sql/qst-36.dot
@@ -0,0 +1,7 @@
+digraph {
+"op_0" ["label"="ticketTable(scan/custom)"]
+"op_1" ["label"="view(__p_0_0=Foo,__p_0_1=Bar)"]
+"op_2" ["label"="view(Foo=__p_0_0,Bar=__p_0_1)"]
+"op_1" -> "op_0"
+"op_2" -> "op_1"
+}
\ No newline at end of file
diff --git a/sql/src/test/resources/io/deephaven/sql/qst-37.dot b/sql/src/test/resources/io/deephaven/sql/qst-37.dot
new file mode 100644
index 00000000000..88dfc495c6a
--- /dev/null
+++ b/sql/src/test/resources/io/deephaven/sql/qst-37.dot
@@ -0,0 +1,9 @@
+digraph {
+"op_0" ["label"="ticketTable(scan/custom)"]
+"op_1" ["label"="view(__p_0_0=Foo,__p_0_1=Bar)"]
+"op_2" ["label"="where(!isNull(__p_0_1))"]
+"op_3" ["label"="view(Foo=__p_0_0,Bar=__p_0_1)"]
+"op_1" -> "op_0"
+"op_2" -> "op_1"
+"op_3" -> "op_2"
+}
\ No newline at end of file
diff --git a/sql/src/test/resources/io/deephaven/sql/qst-38.dot b/sql/src/test/resources/io/deephaven/sql/qst-38.dot
new file mode 100644
index 00000000000..b772a0b58b7
--- /dev/null
+++ b/sql/src/test/resources/io/deephaven/sql/qst-38.dot
@@ -0,0 +1,9 @@
+digraph {
+"op_0" ["label"="ticketTable(scan/custom)"]
+"op_1" ["label"="view(__p_1_0=Foo,__p_1_1=Bar)"]
+"op_2" ["label"="view(Foo=__p_1_0,Bar=__p_1_1)"]
+"op_3" ["label"="sort([ASCENDING(Bar)])"]
+"op_1" -> "op_0"
+"op_2" -> "op_1"
+"op_3" -> "op_2"
+}
\ No newline at end of file
diff --git a/sql/src/test/resources/io/deephaven/sql/query-36.sql b/sql/src/test/resources/io/deephaven/sql/query-36.sql
new file mode 100644
index 00000000000..d9371991550
--- /dev/null
+++ b/sql/src/test/resources/io/deephaven/sql/query-36.sql
@@ -0,0 +1,4 @@
+SELECT
+  *
+FROM
+  custom
\ No newline at end of file
diff --git a/sql/src/test/resources/io/deephaven/sql/query-37.sql b/sql/src/test/resources/io/deephaven/sql/query-37.sql
new file mode 100644
index 00000000000..a334626724c
--- /dev/null
+++ b/sql/src/test/resources/io/deephaven/sql/query-37.sql
@@ -0,0 +1,6 @@
+SELECT
+  *
+FROM
+  custom
+WHERE
+  Bar is not NULL
diff --git a/sql/src/test/resources/io/deephaven/sql/query-38.sql b/sql/src/test/resources/io/deephaven/sql/query-38.sql
new file mode 100644
index 00000000000..f10d0a6aa7a
--- /dev/null
+++ b/sql/src/test/resources/io/deephaven/sql/query-38.sql
@@ -0,0 +1,6 @@
+SELECT
+  *
+FROM
+  custom
+ORDER BY
+  Bar
diff --git a/sql/src/test/resources/io/deephaven/sql/query-39.sql b/sql/src/test/resources/io/deephaven/sql/query-39.sql
new file mode 100644
index 00000000000..6e995cc66f0
--- /dev/null
+++ b/sql/src/test/resources/io/deephaven/sql/query-39.sql
@@ -0,0 +1,4 @@
+SELECT
+  Bar + 1
+FROM
+  custom