Honestly, I don't think we will, no. I don't think the show will have ANY more. First, I think they don't want to run the risk of contradicting movie versions (you may say the apparent contradictions between Rubble's backstories in the show and Rubble & Crew mean they don't care, but it may also have made them actually start being cautious when they realized people DO pick up on this stuff). But second and more important, I just don't think they perceive some pups have an important enough presence in the property to warrant devoting that much time to. That said, they could always COMBINE a pup's backstory with something else. Another pup's that's being introduced, or the background to some conflict.
But yeah - I don't think the show will have any more backstories, and I think the movies will veer off from the pattern of one pup's backstory per movie before they get to Rocky and Zuma. Though we MIGHT see them in combination with something else. I can see there being a mermaid movie that happens to tell Zuma's backstory, for example