Anecdotally, I have heard about gifted kids in split grade classrooms that it became really hard for teachers to ignore that a kid was ready to work right alongside the higher grade kids, and, compared to most, actually above - puts it all in perspective for the teacher, as it were, and the kid basically skipped themselves. The crux being, of course, whether the school might be persuaded into letting him advance with the other fourth graders.
The teachers would have to agree that it would be ridiculous if he were then to remain in the 3rd/4th classroom for another year and essentially have to REPEAT 4th grade.