The attached (encrypted) script is taken from the book I helped to write: https://www.sas.com/store/books/categories/usage-and-reference/discovering-partial-least-squares-wit... and it shows the effect. As the correlation between X1 and X2 near +1 (or -1), the problem becomes ill-conditioned. So I assume the data you have did not come from a designed experiment, and that you will need to drop some variables if you want to use MLR.
