The search for new near-infrared probes for fluorescence imaging applications is a rapidly growing field of research. Monomeric fluorescent proteins that autocatalyze their chromophore are the most versatile markers for in vivo applications, but the development of bright far-red fluorescent proteins (RFPs) has proven difficult. In this contribution, we search for the theoretical limit of the red shift and how it can be reached without sacrificing the fluorescence quantum yield. Through extensive excited-state pathway calculations, molecular dynamics sampling, and statistical modeling using QM/MM schemes, we provide a new understanding of the chromophore's photophysics including the role of its acylimine extension, which is the main difference from other families of fluorescent proteins. The excited-state dynamics of the mPlum RFP and its mutants provide an ideal basis due to mPlum's flexible binding pocket and extended dynamic Stokes shift. We found a large number of structural species with red-shifted emission that differ in rotamer states and H-bonds between key amino acid residues in the binding pocket. By analyzing their spectral and structural features, we derive guidelines for future rational genetic design strategies.