Yes it is very frustrating when you have people getting 2 or 3 days off a week regularly but they won't give you one day off.
Well, it tends to be a problem of short staffing and not a problem due to their arrangement of sharing FTE.
If you have 5 calls and 15 regular shifts for an FTE, it doesn't matter if 1 person does it or 3 people share it. The overall coverage and cost is the same. So if 3 people want to share that, it's their choice and it's not unfair to the rest of the group.
You can't expect to be able to force them to take more call or shifts than their proportional share.
If you don't have enough time off as an FT, then the solution is hiring more FT or PT...not expecting to squeeze more out of the FTE sharing pool of they aren't interested. But hiring will cost everyone a share of the revenue pie, so it's a matter of what you are willing to give up for that time off. Per diems can help if available, but that's if available regularly and reliably which they often aren't