Alpine used to have some quite thin amps. A two channel (MRH-T305), a four channel (MRH-F254) and a five channel (MRH-F255), all 35 mm thick, that's about 1.4".
I used to have the F255 under the passenger seat of my Plymouth Duster. Not great but definitely OK if you are not into high end car audio but dig your empeg for other reasons.