My understanding of the phrase is 'and many more as well as.' So for example 'and many more reasons besides that' means 'and many more reasons as well as the one you have mentioned.' Hope this makes sense :)

"many more besides" is a curious expression that is still used, but not frequently. Here's an example in use, "the tree is filled with oranges, and many more besides" and it means the tree has so many oranges we can't count them. It is also used to compare two quantities or numbers of things, for example, "Brian had a lot of toys, but Tony had many more besides". Once again, we can't count how many toys Tony had. Interestingly, "many more besides" does not mean an infinite number, instead it means we are too lazy, or don't have enough interest, to count them.