Use attached drive for Time Machine for that computer and another

Thank you. I began to assume that since I tried all the combinations and my reading of Apple's documentation didn't mention the possibility.

I now have three partitions on an external hard drive and it seems to be working (will have to wait to make sure backups complete)

1. locally connected iMac
2. for other Time Machines backups. I did create folders and see that there is a sparsebundle. I had done this before reading your post because I was afraid that maybe only one TM backup would be allowed in the partition and I was tired of starting or creating backups and waiting for them to complete and then find out I had to erase the partition. Overkill at this point, but I don't think it's costing much.
3. for Mylio backup/"Vault" which requires its own partition. Mylio is a multi-platform application so often doesn't use all of macOS capabilities.

I rather have as few partitions as possible since it means I have to change the size if one partition needs more space and I may have too large a partition and never use it.

Rant: "If you back up a locally connected Mac, you cannot use that partition for anything else." I didn't notice that in the Apple documentation or when starting a TM backup in a partition. Maybe I missed it. So many repetitive warnings, but not one for something important. Wanting to use an external drive for many TM backups would seem to be a common situation.

Adding a bit more information. For my wife's MBP, I set up a folder (as above) and in "Sharing" gave her permission to read-write to that folder. Then right-clicking on the folder set to allow Time Machine Backups. To help us understand what and where that disk is I gave it a name similar to "Wife TM backup on 10TB HD". Seems like overkill, but on her TM preferences clearly shows which backup it is. Because she also has occasional TM backups to drives stored elsewhere.

I could have missed a step or two because of the convoluted nature of this. For example in Sharing a button "Options" is available and then hidden under a right click is "Advanced Options". Options mentions SMB and Windows. Etc.