SPSS Statistics

Hello everyone! I am conducting the following research:
I want to see if  the number of self-harm incidents (total incidents, 200) in a inpatient hospital sample (16 inpatients) varies depending on the following predictors; ethnicity of the patient, level of care (medium or enhanced) and the diagnosis. I was thinking of conducting a poisson regression as my outcome variable is a count of events, but I am unsure how to account for the proportionality of each predictor. I have read that an offset variable can be added to a poisson regression to account for a varying amount of exposure (either if there is a variation in the observed period of time, or if the sampling size varies across groups). I have read a lot about how to integrate an offset variable to account for time exposure, but nothing on how to integrate an offset variable for different group sizes, which is my case. There are higher rates of white inpatients in an enhanced care setting in the hospital, which is reflected in my sample. I therefore wanted to account for this when conducting the regression, but am not sure if it is possible to add this as an offset variable in SPSS. Furthermore, I would need to account for several predictors (ethnicity and level of care) which I'm not sure is feasible in SPSS, as only one offset variable can be added to the model? 

It would be great to hear about any examples of an offset variable being added to a poisson regression to account for different rates of predictors, or to know if other analyses would fit my research question better in your opinion? Any help would be greatly appreciated! 

Thank you!