2 or more type of categorical variable with multinomial logistic regression

Dear sir

Good evening from Japan
I would like to know about usage of multinomial logistic regression
In my analysis have different type of (2 or more) categorical independent variable and dependent variable. Firstly I select most relevant factor by using some method and second stage I would like to measure the model fitness by using multinomial logistic regression.
That multinomial logistic regression is suitable to use for (2 or more) categorical variables.?
I am waiting to see your reply
thanks you so much for reading my thread