You don't know whether you need a business person, a designer, or a developer? Then the question to ask is why get a third co-founder at all? It will complicate communication, equity, etc., so you should actually avoid a third co-founder until you really need them.
A developer would be great for brainstorming, for building a technically great framework, and for bringing motivation and inspiration to the whole project. I would enjoy working more on the business side of things too.
A third founder with business skills would be great too -- we need to incorporate and do a lot of different business related things such as risk management and research into law and the kind of guarantees we can give to our customers, amongst many other things. If someone else would focus on that I would be more free to develop the actual product.
We can go forward with 1.5 founders as well, but it would be a lot more fun with a third person, would increase the motivation, the speed of iteration, and overall the chances for success!
but i do appreciate our collaboration - it's highly inspiring and working together with him is very helpful for the project. although i do 80% of the work currently.
Look at Youtube as the perfect case study. Jawad, the thrid foudner, gave up operation dutities togo back to school. he still advised, and was paramount in the early stages of the company/product.
If the OP has already found one right partner (it takes more than just chemistry), then losing that person may harm you and your business.
At a same time, a 3rd founder who is a specialist could really help you in this situation. I don't think I can add any more value about that than it's been already said here.
Goodluck and make sure to post updates as to your founder search.
This is your core problem. I can think of two main possibilities: a business problem or a team problem. Either he's not a committed co-founder or your startup's business opportunity is not good enough to pull him in more. Adding a third person won't fix this problem, it will just give you another.
I do appreciate working with my co-founder and he does push the project forward. But since I do 80% of the work, I would appreciate a full-time partner.