Seems like he has a decent case for hall of fame admission, though he never actually won a SB as a coach.
Reeves, Levy, and Bud Grant lost 4 super bowls, but, as Knot points out, Grant's and Levy's were with one team.
I had to look it up, but Shula, Parcells, Reeves, Vermiel, Holmgen, Reid and . . . John Fox have taken 2 different teams to the super bowl. I had to check, but Fox (Panthers, Denver) would be the other one to not win with either franchise.