Blanca E Gutierrez have you reached out to a tracker? There are a few very good ones around here. They may at least be able to offer advice. Here are 2 you could reach out to.
Professional Pet Trackers
Friends of KC Inc.
UPDATE: Max has not returned home yet. There's another post claiming to have found him but they are telling me through text that he doesn't have anymore and that their cousin took him to a vet but won't give me any info more info.