If you look at a not very modern dictionary, as I just have (Shorter Oxford English Dictionary,Third Edition, 1944) You will see: "Outside of: US colloquial - ... with the exception of." And, further, "Outside, (Shortened from outside of)... Beyond the limits of (any domain of action or thought, any subject or matter)."
So, technically, there is no reason as regards usage in 1944 why you should not insert "of" after "outside" in the sentence you quote.
You should also be aware that some native speakers of English cannot see what purpose is served by the particle "of" and get cross when they see it. That is no reason for you not to use it if you wish.