Columns Block: Try adding a "negative margins" block style

assets/sass/05-blocks/columns/_editor.scss

@@ -1,5 +1,47 @@
-.wp-block-columns .wp-block,
-.wp-block-columns .wp-block-column {
-	// Allow Gutenberg to set the width of a block that lives inside the columns block.
-	max-width: inherit;
+.wp-block-columns {
+
+	.wp-block,
+	.wp-block-column {
+		// Allow Gutenberg to set the width of a block that lives inside the columns block.
+		max-width: inherit;
+	}
+
+	&.is-style-twentytwentyone-columns-overlap {
+
+		@include media(laptop) {
+
+			.wp-block-column:nth-child(2n) {
+				margin-left: calc(-2 * var(--global--spacing-horizontal));
+				margin-top: calc(2.5 * var(--global--spacing-horizontal));
+
+				// Provide text-based child blocks with a default background color to ensure they're readable.
+				> p,
+				> h1,
+				> h2,
+				> h3,
+				> h4,
+				> h5,
+				> h6,
+				> ul,
+				> ol,
+				> pre {
+
+					&:not(.has-background) {
+						background-color: var(--global--color-background);
+						padding: var(--global--spacing-unit);
+					}
+				}
+
+				// Lists should still have their usual left padding.
+				> ul:not(.has-background),
+				> ol:not(.has-background) {
+					padding-left: calc(2 * var(--global--spacing-horizontal));
+				}
+
+				&.is-vertically-aligned-center {
+					margin-top: 0;
+				}
+			}
+		}
+	}
 }

assets/sass/05-blocks/columns/_style.scss

@@ -38,4 +38,43 @@
 			margin-bottom: 0;
 		}
 	}
+
+	&.is-style-twentytwentyone-columns-overlap {
+
+		@include media(laptop) {
+
+			.wp-block-column:nth-child(2n) {
+				margin-left: calc(-2 * var(--global--spacing-horizontal));
+				margin-top: calc(2.5 * var(--global--spacing-horizontal));
+
+				// Provide text-based child blocks with a default background color to ensure they're readable.
+				> p,
+				> h1,
+				> h2,
+				> h3,
+				> h4,
+				> h5,
+				> h6,
+				> ul,
+				> ol,
+				> pre {
+
+					&:not(.has-background) {
+						background-color: var(--global--color-background);
+						padding: var(--global--spacing-unit);
+					}
+				}
+
+				// Lists should still have their usual left padding.
+				> ul:not(.has-background),
+				> ol:not(.has-background) {
+					padding-left: calc(2 * var(--global--spacing-horizontal));
+				}
+
+				&.is-vertically-aligned-center {
+					margin-top: 0;
+				}
+			}
+		}
+	}
 }

inc/block-styles.php

@@ -18,6 +18,15 @@
 	 * @return void
 	 */
 	function twenty_twenty_one_register_block_styles() {
+		// Columns: Overlap.
+		register_block_style(
+			'core/columns',
+			array(
+				'name'  => 'twentytwentyone-columns-overlap',
+				'label' => __( 'Overlap', 'twentytwentyone' ),
+			)
+		);
+
 		// Cover: Borders.
 		register_block_style(
 			'core/cover',