My advice to you is to take it to a wig salon that has colorists that know what they are doing. Going dark should not be a problem ,but the wig does have a lot of red and you want to be sure the dye to get it more brown is the right one so you do not end up with a strange color. Also you might want them to do a test on a few hairs before you move forward.
Contact Gardeaux Wigs. google: gardeauxwigs.
Check out Gardeaux Wigs. Gardeaux Wigs is on etsy.com, facebook.com, instagram.com, and YouTube. This lady from Santa Rosa, California, buys 100% human hair, high-quality wigs [mono-filament, lace front, etc.] -- then she cuts and colors them. They all have “roots” and highlights/lowlights. Absolutely brilliant! They can be pricey -- but nobody knows it’s a wig! Beautiful!!
This lady should be able to help you. --