Technically, you can apply to multiple permanent residency applications. However they should not be under the same program. For example you cannot have two PR applications with both being Canadian Express Entry.
But TR2PR and Canadian Express Entry are different. You can apply in both. Same thing for provincial nominee programs, they're different as well.
In this case, it's just the matter of cost. You need to pay application fee plus right of permanent residency fee for the new program. When one of them gets approved, for the other application, you cannot get a refund for the processing fee but you'll get a refund for right of permanent residency fee.
Overall, if the cost is fine with you, you can apply.