How to do Multiple Logistic Regression in R, I know there is "mlogit" package but I have hundreds of variables while "mlogit" does not support "~."...

How to do Multiple Logistic Regression in R, I know there is "mlogit" package but I have hundreds of variables while "mlogit" does not support "~." to represent the rest of variables. The formulas support the Multiple Logistic Regression is in "Elements of Statistical learning" p119 equation (4.17). Please also give me the idea behind the code, as it confused me for days.