The squeeze press is a dumbbell bench press with one difference: the dumbbells are kept in contact with each other at all times and you're actively squeezing them against each other as hard as possible. This shifts all the stress onto the pectorals.
Want to ramp it up? Overload the eccentric (negative) phase. All you need is a good spotter.
Eccentric Tabletop Squeeze Press
I call this movement the "eccentric tabletop squeeze press" because the dumbbells, when pressed together, create a perfect platform on which to rest a weight plate.
The video shows NFL running back Marquell Beckwith doing it with 100-pound dumbbells and a 45-pound plate, followed by my figure competitor Leslie using 50-pound dumbbells and a 25-pound bumper plate. (The proper dumbbell-to-plate ratio is 2:1.)
Simply have your training partner place a weight plate on top of the dumbbells while you perform the eccentric/negative phase of the movement and then have them lift the load off immediately before transitioning into the concentric pressing phase.
Make sure the spotter keeps his hands close to the weight plate so it doesn't slide off.