Classical Thermodynamics restricts engineering. These restrictions are independent of mechanism and kinetics, and thereby inescapable. Forgetting these restrictions can lead to over-optimistic designs for making bio-plastics from waste, and to erroneous ideas on early or new Life on this or other planets. This can be rectified by putting the thermodynamics in place. Is every biochemical network design feasible, provided one puts classical thermodynamics in place? Or, are there other, ill-recognized, generic restrictions to bioengineering? For a while a Non-Equilibrium Thermodynamics (NET) has been trying to discover behaviors of dynamical systems away from equilibrium that are completely independent of kinetics and mechanism and thereby not engineerable. The principles discovered were of limited use to bioengineering however. We here show that processes away from equilibrium must indeed depend on kinetics and mechanism, but, importantly, not on all kinetic and mechanistic details: There are limitations to what the engineering of mechanisms and kinetics can achieve. It is of course better to recognize what is impossible before trying to engineer the impossible. Importantly, the new NET methodology also shows that system properties that are possible, can be engineered only in certain ways. The new NET methodology also enables to understand, and perhaps engineer towards, a performance that, by adjusting the network, remains optimal when conditions are changing. Using our in silico discovery tool, we show that this may indeed occur in the Archeon S. solfataricus. What we call ‘variomatic’ gear shifting is a way that some cells may use to self-engineer their ways to maximal growth rates in environments that lack robust resources, such as in environments with fluctuating oxygen levels. Population heterogeneity is another mechanism that can increase the robustness of a cell factory. We discuss a NET principle that suggests ways in which one can engineer the cells’ diversity. Transcription burst size rather than kinetics should be modulated for making a diverse population perform much better than its average.