Yes, you can push a table up to the island to create this look. A custom piece would usually have the table depth the same depth as the island, and the top of the dining table would be attached to the island with brackets or angle, having one side of the dining table top with a base. But there are no rules to come up with all kinds of creative solutions. Have fun!

Just make sure your table is in proportion to the island. It doesn't have to be connected or integrated.

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if you have control of island width you can make it the width of the table you want, most are a standard width