I would be happy to help with this and thanks for sharing a link to an example website as this really helps everyone understand exactly what you're looking for right off the bat. As you also mentioned, you're using the Supply theme, which natively does not have a multi-column dropdown menu. In order to achieve what you are looking for, you'll need to do one of following:
When checking out the website you shared and clicking on "Shop Color", I noticed that their menu had a little tiny message at the bottom right-hand corner that shared what app they used to achieve this menu, how handy!
When clicking on Smart Menu, it takes me to this app here. Based on it's 4.8 star ratings and positive reviews, people seem to love and recommend this app! The app offers both free and paid versions for you to choose from, meaning you can test this out without having to pay anything to make sure it's a good fit for your shop. Give that a try and let me know your thoughts! I would love to hear if this app does the trick for you.