There are some packages like factoextra and chemometrics in R which can be used to perform Multivariate Statistical Analysis.
For reference, please visit http://www.sthda.com/english/wiki/factoextra-r-package-easy-multivariate-data-analyses-and-elegant-visualization and https://cran.r-project.org/web/packages/chemometrics/vignettes/chemometrics-vignette.pdf
Yes, R can handle all such calculations very smoothly. Every statistical calculation is simply a set of mathematical operations that are performed on data. R like SPSS is a programming platform with inbuilt packages that contain mathematical operations for performing such calculations. However, R also has an added advantage of being free of cost and open source which SPSS lacks.