Although hackchi2 is still being improved, it already allows the transfer of SNES roms to the console, even if the process if very manual for now (this will be improved very soon).
Basically, in addition to installing a custom firmware to the console, typical SNES roms need to be converted to the format supported on the SNES mini: .sfrom. Scripts have been released by the modding community to do just that, and people with enough dedication can reasonably easily add more games to their SNES mini.
Enthusiasts say that with the support of compressed roms on the SNES mini, the device could accommodate a hundred games, making it a nice little emulation station.
The full process on how to run additional games on the SNES mini is described at length here by reddit member viral_dna. Skullator also shared a full tutorial video below:
Skullator says this also works for games that used to require special chips such as Megaman X2.
As pointed out by multiple people, the process is very manual and you could end up with issues. Unbricking the SNES mini seems fairly easy in case of issues with this technique, but proceed at your own risk, or wait for a few days for Hackchi2 to be updated with things that will automate most of this.