I’ve worked with quite a few starters over the past 10 years, some that I bought and some that I started myself. For quite a while I maintained (and used) about 6 different starters. I was able to maintain each starters individuality. It took some care and time in order to do that.
It required keeping each starter in the refrigerator as a “mother” starter, adhering to a schedule of feeding the starter regularly each week so that it never got “old” in the refrigerator, maintaining only a small amount of starter, keeping the “mother” starter tightly covered so that it didn’t get contaminated either from the air or from the other starters. When I wanted to bake bread, I’d refresh the mother starter then remove part to use for the bread and re-feed & refrigerate the mother starter.
I used to run a bread forum on the internet and heard from many who were able to maintain their starters’ characteristics. Others have not been able to. Starters are not expensive to purchase online so it’s probably worth it for you to take a chance with one, if that’s what you want.