” So now I’m wondering if I can do this same kind of thing with other plants that I usually think of as annuals.”
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Many people think of peppers as annuals, but they are really perennials. I have a prize Gypsy pepper that has about 15 almost ready peppers on it now, and it’s still blooming, but the best part is the cuttings that I have been able to start. One of the cuttings is only about an inch or so tall so far, but it already has visible multiple bloom buds! Now my main problem is going to be keeping them alive thru the winter. (”Gypsy” is a hybrid, so seeds are not reliable.) It is the best pepper I have seen for Central TX, and I strongly recommend giving one or more a try if you can find one. Bonnie plants has them on their website, but they didn’t have any for sale this fall.
http://bonnieplants.com/products/vegetables/peppers/gypsy-pepper
For some reason I am recalling that you can take successive cuttings for certain plants, up to 24 -32 generations , depneding on the plant .
Apparently, the genertic code goes all 'wookie-wobbly' between the 24-32 generation cuttings thru gentetic mutations, and reverts back to the original plantings.
Thats not Gospel, but that is how I remember it according to a geneticist at Co-operative Extension.
For example : first cuttings from geraniums can be held over till next year, but flowers will shatter easier, but will be hardier to frost,
and keep producing flowers moreso than seedlings, even beyond a light frost due to genetic mutations . YMMV