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I'd just keep dating and dating I think. I couldn't put a number on it. Maybe infinite.
I actually enjoyed dating for its own sake though. I didn't consider it a drag whatsoever, and enjoyed the woman's company. Each woman I dated often expanded my interests too, like getting me to try new foods, listen to new music, go to new places, try new activities... so every new woman I dated often offered and gave me something that the previous ones didn't.
So I think it'd be a very huge number, at least, before I'd get tired of dating.
It's never going to happen. I enjoy having a girlfriend too much.