I too have a .444 on a Mauser -- except that mine uses blown-out and shortened .30-06 brass headspaced on the mouth of the case.
Articles and releases that announced the then-new .444 Marlin also revealed that the factory was making the .444 Marlin cases from lots the rest of which were on their way to becoming .30-06 cases. At some point along the line, some of the cases being formed were diverted to become .444 Marlin cases, while the rest went on to become .30-06s.
So the only differences were that
(a) the .30-06 cases had more brass removed from the head (forming a rimless case), were trimmed longer, and necked-down, while
(b) the trimming of the .444 cases left more brass in the head (forming a rimmed case), trimmed those cases shorter, and left them straight,not necked.
From this, I assume that a .444 Marlin on an action strong enough to take .30-06 forces and pressures can be loaded to the same maximum pressures as the .30-06, .270, .243, .308, etc.
