Yes is simple answer. But how are you measuring the response, ses health inequalities, how is this measured as an individual variable, inequalities suggests a distri ution not a value.

Kelvyn Jones This is a very good point. I was considering using the concentration index to measure educational health inequalities and looking at whether 4 components of access too healthcare abundantly defined in the literature (affordability and acceptability measured from DHS household level, and accessibility and availability - country-level data) builds onto the inequalities. Is that feasible?

I think it would be helpful if you could formulate your task in terms of variables and regression equations.

Regression equations can include the same parameters for different dependent variables. But I think the simplest approach is just to start with a classical linear regression to see what happens. Why do you need the multilevel/cross-sectional modelling? Try to consider each dependent variable separately: if you have a lot of observations, maybe you can just use standard approaches without multilevel modelling.