Correct model for outcome variable with 4 categories

#1
I am working on a study that measures the association between BMI(exposure) and multi level(outcome). I am testing with BMI both continuously and categorically, but the outcome is a score with 4 levels. I am having trouble deciding on correct regression analysis for an outcome of 4 levels. If necessary, I can change to dichotomous, but I feel my findings would lose some power. Any suggestions?
 
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#3
I wanted to use ordinal logistic regression, but the proportional odds assumption failed. Is there anything else anyone has in mind?