Fitting with one common and some different parameters over a series of measurments in python

Question

here is the problem again, i hope now its clear to everybody. I have some samples data, lets name those j. For each sample of data, i have a theoretical modell, that i can fit to the data. For the sake of simplicity, lets name the fitting function f(sig1, µ1, sig2, m2). Of course, as the data for each sample is slightly different, i get from each sample a different sig1, µ1, sig2, µ2. And here comes my problem: I need the µ1 to be the same i each measurment, but i don't know it in advance. Of course, i could now fit every sample j, just take e.g. the mean of µ1 and the fit them all again, but that is not the best approximation. So, i want to fit µ1 global for all my measurments at the same time and all my other parameters for each single measurment. i hope my question is clear now.