Including more explanatory variables seems irrelevant hereI do not think the problem comes from the small sample size per. The problems you encounter are very likely to come It rather comes from the fact that presence/absenceMPs are obviously almost present everywhere regardless from the value of MP is not an appropriate response variable, i.e. it might not represent muchexplanatory variables, since only 6 samples out of 30 have a score of 0, and all the rest are 1s. Therefore, thereThere is barely any variance to explain. Therefore, including more explanatory variables seems irrelevant here.
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.