How can I swap data between two computers using Time Machine?

ziggy's papa wrote:

We Have two computers. I would like to trade computers with my partner. Is there any way to transfer all the data off of the one and on to the other and vice versa? Would Time Machine do the trick?

This is an odd request. I have never done that but I think this would work:

(1) Make Time Machine backups for each computer (use separate external drives for each of the backups). It would be wise to have at least two backups for each Mac in case something goes amiss. Test each backup by restoring a few random files and folders to the Macs they backed up.

(2) Follow this for each Mac: What to do before you sell, give away, trade in, or recycle your Mac - Apple Support

This basically restores each Mac to factory settings, like it was when it was new. Make sure you pick an option to install the most recent version of MacOS that was on the Mac when the Time Machine backup was made.

(3) Each Mac will now be like it is a "new" Mac. On first boot up, you will be asked questions about migrating from a Time Machine backup. Indicate "yes" and connect the appropriate Time Machine backup.

I have done the above many times with a truly "new" Mac right after purchase. Since you will be following Apple's instructions for restoring each Mac to factory fresh condition, it should also work as it does on actually new Macs.