Cox proportional hazards with multiclass dependent variable

Is it possible to perform a multiclass Cox proportional hazards model? I’m interested in finding the probability of self cure on consumer loans, or just study how self-curing clients behave so as to identify future customers that behave the same way. My dependent variable of interest has 3 classes: -not cured (0) -cured after being contacted (1) -self cured (2)

I was thinking maybe two regressions have to be run in this case (similarly as in the multinomial logit), one where it’s 0 vs 1, and another where it is 0 vs 2, maybe another 1 vs 2?

I tried looking for this but I didn’t find anything, so I’m wondering if it’s possible at all?