Including more explanatory variables seems irrelevant here. The problems you encounter are very likely to come from the fact that presence/absence of MP is not an appropriate response variable, i.e. it might not represent much, since only 6 samples out of 30 have a score of 0, and all the rest are 1s. Therefore, here is barely any variance to explain.
I would try to obtain a continuous measure of MP instead. If this is not possible, I would not run any statistics, but simply say that MP can be found in most samples regardless of the value of the explanatory variables.