For a conventional power transformer operating at 50 or 60 Hz, the core (magnetization in laminations) loss can increase only when
a) The primary
voltage is increased (don't use a 120 Vac transformer on 220 Vac)
b) the primary frequency is decreased (Don't use a 60 Hz transformer on 50 Hz unless the mfgr states 50/60 Hz)
c) the number of primary turns is decreased (decreases inductance).
The core loss is determined entirely by the design of the transformer as an inductance w/o a secondary winding. The core probably goes up to ~1.4 Tesla peak; any increase will significantly increase losses.
Bob S