Now that you've had a day of rest, you should be ready to get back into the gym for another tough lesson with the iron. Grab a dumbbell and let's get going!
The overhead press is a total-body movement. True, your shoulder will bear the brunt of the weight, but your core, glutes, even your quads should be tight, tight, tight. Your shoulder will be much better supported and thus able to lift more weight when the rest of your body is active in the lift.
In reality, your core should be active in almost every movement you do. For example, the loaded carries can't be done well unless your abdominals are tight and your back is set. If you're hunched forward, you're not helping your shoulders grow and you're putting yourself in a position for likely injury. Stay athletic!
Don't forget to pay special attention to the rest periods. They're short for a reason. Not only are we building muscle, we're stressing the cardiovascular system so we can improve all aspects of our fitness.