Hi,

I am not sure if I understood totally the scenario. But I will share some ideas.

Product Backlogs are related to everything that needs to be done to develop a Product. Regardless how many teams work on it, ideally is one single Product Backlog.

If you have 3 solutions so to say and they are worked by different teams, but they have strong dependencies with each other. I would suggest a single Product Backlog. If the solutions have no relation to each other whatsoever, then, split into different Product Backlogs.