Can a Temporary Resident Permit cover more than one ground of inadmissibility at the same time?

Yes. A TRP isn't limited to addressing a single ground of inadmissibility — if a person is inadmissible for more than one reason at once, for example both a criminal conviction and a separate medical or financial concern, a single permit can be issued to authorize entry or stay despite all of the identified grounds together, provided the officer is satisfied the overall justification outweighs the combined risk.

This doesn't mean multiple grounds are simply averaged out or treated as less serious together than individually — if anything, an officer weighing several grounds at once may look even more closely at the overall picture, since each additional ground adds to what has to be justified. The application needs to address each relevant ground clearly rather than focusing on just one and hoping the others are overlooked.

Because a permit covering multiple grounds involves a more complex assessment, and because missing or downplaying one of several relevant grounds can undermine the whole application if it's later discovered, anyone in this situation should make sure every applicable ground of inadmissibility is identified and addressed directly in the application, with legal advice, rather than presenting only the most obvious one.