The first station having the calls is who controls anyone else getting them. Permission can be granted - and charged for the privilege - by the original station with the calls.
Depending, the original station may have to make a license modification.
An AM never has a suffix, AMs are always “WXXX”. This allows for a FM, TV, and AM with the same calls.
WXXX-FM, WXXX-TV, and WXXX.
LPFM always has the -LP suffix. There could be a WXXX-LP owned by a fourth party and all four stations share that same call sign.
If there is no AM but there is an FM & TV, one of them can be suffixless.
example, in Greenville, NC:
WNCT 1070
WNCT-FM 107.9
WNCT-TV 9
They originally had the same owner but all three are owned by separate parties now.
another example:
WCMC is an AM in Wildwood, NJ and WCMC-FM is in Raleigh, NC (technically Holly Springs licensed)
they have never had any relation to one another, so WCMC in Wildwood would have had to give the Raleigh FM permission to use those calls.
Let’s hypothetically reverse that last one and say that WCMC existed first on FM in Raleigh, without the -FM suffix. If the AM in Wildwood wanted those calls the Raleigh FM would have had to grant permission, and change their license to have a suffix - becoming WCMC-FM - since an AM never has a suffix.