yeah it can go either way. since MSres=  SSres /(n-p) where n is sample size and p is no. of predictors {i.e. no. of independent varaibles (k) + 1}. since SSres always decreases as p increases, MSres initially decreases, then stablizes, and eventually may increase. so increasing independent variables may decrease or increase the F statistic and thats the reason we choose the model with minimum MSres while selecting a model out of different models with varying number of predictors in multiple regression analysis based on MSres or Radj criteria. hope that helps.