I've been squarely in your shoes before. I own mainly SFHs that are concentrated in one region, with several of those in one town, and several of those in the same neighborhood. That neighborhood is where I started out, and I've managed to accumulate several there because of favorable numbers, but I've also made an effort to diversify, trying not to sacrifice returns.
You are wise to consider some diversification by investing in a different part of town, a different town, the countryside, etc. But.... if you (and your partner if you remain tied to him) have the funds ready to pull the trigger on the next deal and you have the opportunity to buy a place that will bring monthly rent at over 2% of the purchase price.... that's pretty hard to pass up. A handful of properties that produce that kind of cash flow can help fund other ventures down the road as they become available. If growth of this business is an important part of your strategy, securing some very high cash flow places early on will be extremely valuable.
I'd continue to look hard for other areas that may meet your criteria in the near/intermediate future. If you find a specific deal or even an area that has potential see what your partner thinks when presented with a real (less hypothetical) option. If he still balks, there's no reason you can't take that route on your own. But until you find something else worth your time and money I wouldn't be afraid to add more holdings in that same neighborhood.
Even if things (rent rates and/or property values) start to decline in that neighborhood, the cash flow is so good now that even a few good years of owning a place like that may prove worthwhile. It sounds like you have a good thing going with your partner. But a word of advice. If you two disagree about a growth/expansion strategy, that's no big deal.... you just don't do the next deal together. But an exit strategy requires more planning. The places you are buying will probably make sense to hold for a long period, so hopefully you aren't "forced" to sell by market circumstances. But at some point, one of you may think that it makes more sense to sell one of your holdings and put that money in a better investment. You may be presented with a sweet deal that he doesn't want any part of. But what if you can only make that deal happen by selling/exchanging your investments with him? Just something to think about. I would consider any deal with a partner, no matter how cordial, to have some risk because of challenges presented when an exit strategy needs to be employed.