Hi Statalist

I am wondering what are the possible options for modelling endogeneity in a multinomial logit model?

My mode is described below:

y1=a+by2+cX

where y1 is a categorical variable with 3 categories (1,2 and 3)

y2 is the endogenous explanatory variable which can take values 0 or 1

and X is the list of exogenous explanatory variables

As a first step, i have used Multinomial Logit and reported results as Average Marginal Effects.

Given that y2 is endogenous I have identified an IV z1 (also a binary vairable which takes values 0 or 1) which can be used in its place (The endogeneity may result from y1 and y2 being determined simultaneously and self selection)

One possible model I have identified is
Control Functions Methods (Jeffrey M. Wooldridge Journal of Human Resources, Volume 50, Number 2, Spring 2015, pp. 420-445)

My questions are:
1. Can i use Control Function Methods to model this, I am a bit unsure about this as both the IV and EEV are binary variables but the dependent variable is a choice variable?

I have used the following code:

reg y2 z1 X
predict y2_res, residuals
mlogit y1 y2 z1 X, base (2)

2. Will the margins calculated after the above code be interpreted in the same way as from a usual mlogit estimation?
margins, dydx(*) predict(outcome(1))
margins, dydx(*) predict(outcome(2))
margins, dydx(*) predict(outcome(3))

3. What possible alternate models could i use?

Thanks
Utterly confused and then a bit more
Mehwish