We have numerically investigated the behavior of the fundamental mode of a step-index, multimode (MM) fiber as the optical power approaches the self-focusing limit (P(crit)). The analysis includes the effects of gain and bending (applicable to coiled fiber amplifiers). We find power-dependent, stationary solutions that propagate essentially without change at beam powers approaching P(crit) in straight and bent fibers. We show that in a MM fiber amplifier seeded with its fundamental eigenmode at powers <<P(crit), the transverse spatial profile adiabatically evolves through a continuum of stationary solutions as the beam is amplified toward P(crit).