We consider experimentally and theoretically a refined parameter space in a laser system near the transition to multi-pulse mode-locking. Near the transition, the onset of instability is initiated by a Hopf (periodic) bifurcation. As the cavity energy is increased, the band of unstable, oscillatory modes generates a chaotic behavior between single- and multi-pulse operation. Both theory and experiment are in good qualitative agreement and they suggest that the phenomenon is of a universal nature in mode-locked lasers at the onset of multi-pulsing from N to N+1 pulses per round trip. This is the first theoretical and experimental characterization of the transition behavior, made possible by a highly refined tuning of the gain pump level.