Thanks for your quick response. I really like your idea of adding the 2nd drive and having both drives doing Time Machine duty. When I noticed that the 2TB USB drive that I use for Time Machine backups was getting very full, I researched the issue a little and was under the impression that Time Machine would simply delete older backups (going back to 2015) to make room for the new ones. However, the 2TB drive now shows "0 MB Free" and will no longer perform backups. I guess it stopped dropping old files. So I got a 4TB drive to deal with it. I wish I had known about simply adding another drive before I started to transfer all of the data from the old drive. Given the "backup failure" messages from Time Machine using the 2TB drive I assumed that it would not take anymore data. But you are saying that by adding the 4TB drive and leaving the 2TB in place, that BOTH drives would be used and that the full 2TB drive would not cause a "backup failure?"
Right now I am getting a message that says "Preparing to copy to "Seagate 4TB Time Machine" and the number of items to copy has been slowly, but steadily increasing. It took about 10 minutes to show 125 items. It seemed to stick there for awhile, then started to slowly increase. It's now been at 169,004 items for the last 10 minutes after about 2 hours total.
Looking at the Activity Monitor, if I am reading it correctly, it shows: Data read/sec 229 KB and Data written/346 KB. However these figures change all the time. Data read/sec can be 0KB and Data written/sec can be 3.0 KB. It's all over the place.
At this point, I think I will give it 24 hours and see what happens. If it stays stuck or does not progress at an encouraging rate, perhaps I will pull the plug and reformat the 4TB drive and try your suggestion.
BTW.. my MacBook Pro is a late 2013 and I believe has 2 USB slots (USB 2.0 not 3.0)