[Epa095]

Traditionally what a 'independent MP' would do is create a new party. Usually it requires a certain number of signatures, not from people supporting them, just supporting their right to become a party. Then they need to have candidates for the ridings they want to be in.

One example is the Norwegian party 'Patient Focus' which

  was formed in April 2021, as a support movement for an expansion of the hospital in the town of Alta in Alta Municipality in Finnmark county, Norway. In the 2021 parliamentary election, it won one of Finnmark's five seats in the Storting (Parlament). 

https://en.m.wikipedia.org/wiki/Patient_Focus_(Norway)