Can I apply to more than one province's PNP at the same time?

You can generally hold expression-of-interest profiles in multiple provinces at once — that part is allowed and common. However, you cannot hold two active nominations at the same time, and once you accept a nomination you are declaring a genuine intention to settle in that specific province. Some provinces also ask whether you have applied elsewhere, and you must answer honestly. Keeping several profiles open is a fair strategy; committing to a province you never intend to live in is not.