The so called "4+3" was only used on the C4 cars, from '85, to around '89.
It is basically a regular 4speed manual, with an overdrive unit bolted to the rear. It was made by Doug Nash, and wasn't the most robust design ever. Actually, the 4speed part is fine, but the O/D unit is junk, imo.
If you are contemplating buying a C4 with the 4+3, be sure to ask lots of questions about the service history of the trans...most folks NEVER bothered to service the O/D unit, which causes major failures.
It operates in a manner that helps with fuel mileage. The trans is shifted just like a normal standard trans, 1-2-3-4. In 2-3 and 4, the O/D unit can be applied, creating the "extra" 3 gear ratios. The O/D unit was controlled by the computer on the first models, then it was driver selectable on the later cars.
Repairs on the O/D unit can cost a bundle...parts are hard to come by, and the labor to build them is steep. There is a place in NY that does carry just about any part needed for the O/D section. The problem is, he KNOWS he's the only one that has them, so he don't sell the stuff cheap!
hth
______________
Joel Adams
C3VR Lifetime Member #56
My Link
(click for Texas-sized view!) NCRS
"Money can't buy happiness -- but somehow it's more comforting to cry in a CORVETTE than in a Kia"