bluetooth – Quickly swap Apple Magic Keyboard between computers?

I have a Logitech MX 80 wireless mouse that allows me to swap between my two computers quickly by just changing the source on the bottom. I am wondering if the Apple Magic Keyboard has a similar functionality? Currently, my approach is to disconnect the keyboard from bluetooth on computer 1, then turn off the keyboard, then turn it back on, then connect it to the other computer. I swap between the 2 computers really frequently, so currently this process takes up a lot of time.