Many regressions: unique (stable) function for exponential and s-shape behaviour

Also, I assume that the reparametrizations we discussed previously (GLM with growth function - problem of indetermiinability when slope = 0) didn’t help - do you have any insights on what was the problem? In the time-series case with a small number of regulators it seems to work OK across all the regimes, but I will hopefully try to extend to the steady-state case in near future, so any insight would be valuable.