I presume (again as I haven’t done it or seen what happens if done) - that if you simply open an account - nothing will happen as you haven’t “cheated” any tax provisions.
However, if you were to pay in - and receive tax-free interest, and you then went over your PSA (for arguments sake say you were an additional rate tax payer so you don’t have any) - you may have to account for that tax free interest. That would be how I see it anyway - although again I have no real way of knowing.
EDIT: found an article from back in 2015 - Paid into Two ISAs