  Some hydrogen-rich core-collapse supernovae (type IIP SNe) exhibit evidence
for a sustained energy source powering their light curves, resulting in a
brighter and/or longer-lasting hydrogen-recombination plateau phase. We present
a semi-analytic SNIIP light curve model that accounts for the effects of an
arbitrary internal heating source, considering as special cases
$^{56}$Ni/$^{56}$Co decay, a central engine (millisecond magnetar or accreting
compact object), and shock interaction with a dense circumstellar disk. While a
sustained internal power source can boost the plateau luminosity commensurate
with the magnitude of the power, the duration of the recombination plateau can
typically be increased by at most a factor $\sim 2-3$ compared to the
zero-heating case. For a given ejecta mass and initial kinetic energy, the
longest plateau duration is achieved for a constant heating rate at the highest
magnitude that does not appreciably accelerate the ejecta. This finding has
implications for the minimum ejecta mass required to explain particularly
long-lasting supernovae such as iPTF14hls, and for confidently identifying rare
explosions of the most-massive hydrogen-rich (e.g. population III) stars. We
present a number of analytic estimates which elucidate the key features of the
detailed model.
