However, all of the patients have one of the predictors (X1), so I know interpreting the intercept of the empty model provides the probability of this predictor (X1), 27% have outcome of interest.

Now when I examine the other 9 known predictors, 2 are significant in my sample (X2, X3). So I know patients can have between 1-3 significant predictors. Is there any other way I can present the intercept besides the probability of the outcome or do I always just report my odds ratios for the other two significant predictors as the odds of Y are 10 times greater for X1 patients when they have X2 and you control for X3? And vice versa.

Also, it seems like I would never know if there was an interaction between X1 and any of the other variable because I do not have data for the reference group for X1. I feel I can move forward, but wanted to see if anybody has any insights or suggestions!