In R, can I integrate different classifying algorithms in one bagging model?
What you're looking for is called an ensemble model which means it is a compilation of several models to improve the results. This is a very common technique for winners in Kaggle competitions. Since you're using R and caret is a popular way to do ML in R, here's a package just for that purpose on caret:

https://cran.r-project.org/web/packages/caretEnsemble/vignettes/caretEnsemble-intro.html