Yes, I agree that just focusing on Rep-Detects and Replicants only would be too limited. But how would it be possible to expand further without loosing the core of the setting? Well, I’d bet my money on L. A. as a neon noir metropolis. That’s actually a third more or less mandatory element in the Bladerunner setting. If you still want a case structure of the scenarios, you could play as either private detectives or as another LAPD unit (homicide?). I’d actually put that possibility in the basic rules since those options are just as noir as the Bladerunners. I guess the LAPD will have to be included in the game anyway.
Another possibility could be to work with a couple of noir style locations instead of working with a group premise. It could for example be a gambling den, a shady strip bar, the Bradbury Building (where J. F. Sebastian used to live), a local police station, or an entire neighbourhood like Little Tokyo (I just assume it’s still there because I think it would fit the setting). Places or neighbourhoods like that could be modular like the adventure sites in Forbidden Lands or the zonesectors in MYZ. The PCs would then be involved in some kind of events, just because they are the kind people who are around in those places. They wouldn’t need to be together in a group or crew.
A third and perhaps more vague city based concept, would be people who spend a lot of time in their spinners (flying cars). You would then get into action while driving, and the drama would be either along the road (spinner chase could be cool) or at certain reoccurring noir style locations that could be spread out along your route. I imagine this would be more of a sandbox take on the setting. The PCs could for example be cops, taxi drivers, car thieves or maybe replicants on some kind of rescue mission. They wouldn’t need to be in a tight crew or unit to make it interesting. It could be a cool premise where you should be able to repair and upgrade your spinners. Or just buy or steal a new one. And driving is for sure a noir thing to do. I actually think the basic rules will need an entire chapter about spinners, driving and roads (routes?). That’s how you are supposed to get around in L.A.