Push ups are a much better exercise then the bench press. You can use weights (put them in a backpack and wear the backpack) to increase the intensity. I personally do weighted press ups on gymnastic rings.
That's one way to go. Another way, that doesn't require added weight, is to elevate the feet on a bench and do them very slowly, with a full range of motion, touching the upper chest lightly to the floor at the bottom of the movement and not resting for even a second with locked elbows at the top of the movement; fluid throughout. All the while observing the checklist I posted above. Depending on how slow I go, I can go to failure by about 20 reps, and I mean true failure. (Without a spotter!) Years ago, when I didn't have ready access to weights for a while, I used to do push-ups for reps. Many, many of them. But this is better.
This thread inspired me to try air squats. They are great! I have improvised the standard method by using a lightweight pair of 5lb dumbbells. When I extend my arms on the down movement, the dumbbells help to offset my weight so I can squat lower and keep my balance. These air squats are a very simple and no-frills exercise that have probably been overlooked by me and others who tend to focus on weights and machines instead of some basic bodyweight exercises that also have their place.
One idea is plyometric pushups. The idea is that you not only need strength to bench press but power and plyometric push ups can work on your power to get the bar up with speed and can allow you to lift faster. I agree that doing 100 pushups with some ease will not translate into strength gains as your pecs are already conditioned. But people forget the power aspect of heavy lifts and plyo push ups really will help. Do the down cycle of a push up and then explode up to a clapping hand or touch your shoulders. If you eventually can get 10-20 should touch push ups then try Superman push ups. Instead of training your chest for pure strength, you can add the power element to get more press and lift more overall weight.
Just as barbell benches are better than machines, I think dumbell benches are better than barbell. Same principle.
I had to youtube “Superman push ups”. My shoulder joints and elbows are hurting just watching that. Looks like a recipe for a torn labrum and elbow tendonitis I’ll leave it to the young guys to do that stuff.
It certainly is the extreme but just plyo push ups get the job done. Can do them on the flat side of a BOSU ball to reduce the strain.
The gains keep on coming. Must be the sardines. I was in full beast mode today and even had to let out a manly groan as I benched. Not all that unusual at my gym,(World Gym), which doesn't have the Planet Fitness no groaning rules which seem idiotic to me, but whatever. Pull ups still suck. Can't do one good one, but I'm improving there too. Building more muscle and staying steady at the waistline. Almost look good naked, for an old guy, which ain't real easy.