Breaking it into multiple formulas the way you did would imply a multivariate model, which we don’t have here. But if we just put the formulas in f1 and f2 into the same bf call, it should be close to working. The only thing that needs to be fixed is that a formula can either be parsed in a standard or non-linear manner. That is,
gamma ~ (1 | lev2cor | gamma_groupings) + mugamma
is invalid as it both contains standard parts and “non-linear” parts (mugamma). If you want an additional formula to be parsed in a non-linear manner, just wrap it in nlf, for instance nlf(gamma ~ phi + mugamma) and then phi ~ (1 | lev2cor | gamma_groupings).