This work illustrates predominant measureable nonlinearities in photomultiplier tubes (PMTs) and introduces a controllable one called "Superlinearity," signifying both a positive nonlinear response and the ability to extend linear operation by counteracting gain saturation mechanisms - charge depletion, space-charge field limitation, and secondary emission surface effects. Recognizing superlinearity and its effect on the temporal step response leads to a true definition of linearity, free of a small-signal linear assumption. Furthermore, given the prevalent use of glass microchannel-plate (MCP) PMTs in favor of a faster impulse response in spite of a small charge limit, we are motivated to examine their nonlinear amplitude response and deploy tailored gain bias string methods to fully harness the maximum linear gain as is usually done for transmissive metal mesh and reflective metal dynode PMTs. Our characterization methodology applies standard NIST-traceable calibrated laboratory equipment with absolute input-referenced techniques, examining step responses over many orders of magnitude in controlled illumination. By doing so, we quantitatively reveal the superlinearity strength independent of charge depletion, yielding true linear responsivity and effectively doubling the small-signal linear limit; this is very relevant to PMT modeling and charge deconvolution efforts. With further development, the tailoring strategies we introduce could be applied to MCP detectors, extracting all useful capillary charge with a significant improvement in large linear signal quality.