Best Method for Data Analysis on a 100 numerical IVs and 200 numerical DVs

I think I might need the help of this valuable community for a task. I have been given a dataset for 100 numerical independent variables (IVs) that predict output for 200 numerical values (from monte carlo simulation results). Which statistical technique should I start exploring and trying on my dataset? The number of observations can be increased for more points to enhance learning an algorithm. From this, I would like to learn a few insights, such as the multiple collinearity among IVs, their overall contribution to dependent variables.

Thank you very much.