Recently, we proposed a dynamic multi-bed PET imaging and analysis framework enabling clinically feasible whole-body parametric imaging. The standard Patlak linear graphical analysis allows for efficient modeling of whole-body tracer kinetics by directly estimating the uptake rate constant Ki and blood distribution volume V, based on a common two-compartment kinetic model. However, this model does not account for reversible uptake (e.g. dephosphorylation in FDG), thus underestimating Ki in this case, a finding observed in a number of published FDG or similar tracer studies. We propose a novel generalized PET parametric imaging framework enabling truly quantitative whole-body Patlak imaging including in regions exhibiting reversibility. For this purpose: a) an extended non-linear Patlak model has been utilized, enriched with the net efflux rate constant kloss, (b) a basis function method has been applied to linearize the estimation process through a computationally efficient algorithm, and (c) a hybrid Ki imaging technique is introduced based on the Patlak correlation-coefficient to enhance robustness to noise. Our evaluation included both simulated and real subject clinical studies. A set of published kinetic parameter values and the XCAT phantom were employed to generate realistic simulation data for 2 dynamic 7-bed acquisition protocols (0-45min and 30-90min post-injection). Quantitative analysis on the Ki images suggests superior quantitative performance of the generalized Patlak in comparison to the standard Patlak imaging in both acquisitions, even when kloss is comparable to Ki. In addition, validation on three dynamic whole-body patient datasets demonstrated clinical feasibility and increased focal uptake with potential for enhanced diagnosis and treatment response monitoring.