TL;DR Probably not practical with consumer-grade fans
In theory, you could make your own. Essentially a "Universal Remote" like for a TV/VCD/DVD/Cable Box/etc. The problem is that it is likely (but I can't say for 100% for sure) that all remotes/receivers for a given brand of fan will use the same codes. A remote works by sending a signal (typically either infrared or an open radio band (like portable (not cellular) phones, WiFi, etc.) with a short code. For non-critical items (TV, VCR, DVD, cable box, fan/light, etc.) the codes will be set by manufacturer, device type and (sometimes) particular model. That is how a "Universal Remote" works - the maker of the remote knows that, for example, all Sony TVs or Panasonic DVD players or whatever use a particular set of codes. The problem is that those same codes will then work for 2 VCRs of the same type (I know someone who used to have that problem) or for 3 fan/lights of the same type. With infrared controls you can sometimes get around this by careful aiming of the remote control, possibly combined with some material installed around the remote transmitter and/or the device receiver to require a more direct aim of the remote.
There are some ways around this when security is an issue. The classic example is garage door openers, and key fobs used to open cars use even more sophisticate solutions (or not - there have been some problems...) Methods can include unique codes, though copying can then be an issue, changing codes (each use triggers the next code in sequence and only the 'n' most recent codes will work at any given time) or encryption of the signal. But increased security has a real cost, so for the fan/light in your bedroom, a simple static per-manufacturer/model code is more likely to be the case.
In some more sophisticated similar situations (think laboratory equipment), there will be an ID # assigned to each device for control purposes - anywhere from 4 to 16 to 128 to 256 IDs. Each device would be set using dip switches (the old days) or a configuration panel of some sort. But that would be overkill for a typical consumer fan/light - normal installation is either one per room (and the walls shield accidental activation from another room) or "all the same is good" - e.g., a series of fans above a large room.