Simultaneous Variants in Commerce
As mentioned on Slack, the best approach to this currently is to set up all your variants and then use the plugin MultiAdd https://github.com/engram-design/MultiAdd to set up a form that can handle this.

Example code is in the ReadMe there.

It uses a single fast controller to update the cart all in one go, so there's no real speed penalty, and it raises events onMultiAddToCart etc. if needed too.