There are two sets of muscles that contribute to the basic act of breathing. Most of us only use one of them effectively.
The diaphragm is a muscle wall extending across the abdomen. When you are sitting around, sleeping or doing regular activities, your autonomous body systems cause these muscles to contract one way, "pulling" the muscle wall downwards. This "pulls" vacuum by expanding your lungs, thus drawing air into same. A second set of muscles moves things the other way, expelling the breath.
Controlled, this can do a good job both of keeping you oxygenated, purging your blood of carbon dioxide and of (if you have any class) blowing through a bass clarinet.
Less known are the "accessory muscles of respiration", as I have had them termed by one of our occupational physicians (when at work, I work for OSHA). These muscles pull from your back around the front of your rib cage, expanding the chest by tugging the ribs "open".
You can make these work by first taking in the deepest breath you can with your "stomach", and then, while "holding" that breath, "expand" your chest. It takes a bit of practice, but once you have it down, you can call it into play whenever you want. If you ever have to have a lung capacity test, try it for one of the attempts, just to see how much more you can deliver.
I learned this trick when playing hockey as a kid. Our coach advised that, when skating up to a face-off, to do the extra "expansion" on top of a normal breath. You get a little more total volume inhaled, thus "super-oxygenating" your blood to a slight degree.
It's not practical to do this with every breath, but the more you carry in, the less likely you will be left short. On the baritone, I use this when doing something like the held note under the "These little town blues..." lyric in New York, New York. Since the bass bone and I are handling a lot of the harmonic foundation at that point, we both work through the half notes preceding, and (just before hitting the pedal tone), do both diaphragm and accessory breathing to get a really BIG lungful.
It's not something that you do all the time, but once in a while it comes in handy.