Yes, I press the side of the grip with my support hand, but after many ,many years of shooting both tactically in the military and training LEOs, along with competitive shooting I have come to realize it depends on the actual gun you are shooting; when shooting my all-steel 2011 I noticed that I could run a less firm grip on fast short to mid-range targets but still had to have a solid grip for long shots; now when I shot IDPA with my M&P Pro in 9mm, I really have to bear down with my left/support hand for all mid to long shots and have a consistently strong but even grip for short range targets also; here is the reason why- you can talk about all these different grip techniques until you are blue in the face, but reality is, depending on what your side your strong hand is (mine if my right hand) when shooting a gun with a plastic frame, (unless you have meat hooks for hands) you must bear down with your support hand, because.... you are naturally going to grip stronger with your strong hand, its the way we are as human beings, are strong hands are called just that for a reason!!!
So under stress you will naturally grip stronger with the strong hand, and you have to compensate that by gripping what I call 85/15 grip; I put as much pressure with my support hand as I can which is about 85%, and as little pressure as I can without losing control with my strong hand, that tends to allow my hits to be center mass a majority of the time and trust me, I have tested his numerous times, when I grip evenly with my M&P, my long shots are ALWAYS to the left side of the target, when I use my 85/15 method, the shots are almost always (97%, sometimes you just pull a shot now and then, which I can usually call, but that's another conversation) center mass in the zero down circle or A zone, depending on which targets I'm using. Now, the key here is I have to consciously tell myself during my walk-thru were I will be gripping STRONG and were I will be gripping more evenly, THIS IS KEY. You can program yourself to do this, its done all the time at high levels of shooting.
Off-hand or support hand shooting is a different game entirely, so you will have to practice your grip for that differently, I can tell you I grip my guns in single hand shooting as solid as I can without pushing the gun off target and I use a good index set-up on the targets. You will also need to practice transitioning because its different when shooting off-hand, I always transition toward the center of my body (if possible based on stage design) because that is stronger then transitioning away from center, i.e. if shooting with right hand, my transition from target to target is right to left, and its opposite if shooting with my left hand. Hope this helps, let me know how it works our for you, and you will need to practice it! and don't let the people who say this has already been answered bother you; if that was true, then we wouldn't need all of the instructors out there teaching this stuff over and over again.
BTW, here are my creds: plank holder with the Small Arms Readiness Group, the USAR version of the US Army AMU; former US-ARNG State Combat Rifle Champion; former USAR Service Rifle Developmental Team member; classified Expert in NRA Service Rifle; Classified Master in IDPA and classified A class in USPSA/IPSC. Member of the US National IPSC Team/Senior Std. Team for 2011 World Shoot; Once I shoot for my steel classification, I'll probably make Master there but my time has been slim this year as I am also still serving in the USAR as a Command Sergeant Major, 38 years and counting, and I have two grandsons that take up a lot of my time. see you on the range!!