My MTB tires say "Inflate to 50 PSI". Can I inflate them a little more for commuting? I bought this MTB for commuting. Yup, I found out later that I should get a road bike instead. Too late. Not planning to use on rough terrain. Can I inflate the tires more than the manufacturer recommends? If I can, how much?
How wide are the tires compared to the rim? Wide tires at high pressure put stress on the rim’s sidewalls which can result in sudden, catastrophic failure. If the tires are relatively narrow it’s probably okay to over-inflate, but I doubt you’ll see much benefit. There are diminishing returns for rolling resistance.

See for example this test of 56mm wide Vittoria AKA tires https://www.bicyclerollingresistance.com/mtb-reviews/vittoria-aka-2015 which have a very high rolling resistance to begin with:

Rolling Resistance Test Results (Speed: 29 kmh / 18 mph / 8 m/s, Load: 42.5 kg / 417 N)
Inner Tube  Conti MTB 29 (225 gr butyl)
Rolling Resistance 55 psi / 3,8 Bar     35.6Watts
CRR: 0.01067
Rolling Resistance 45 psi / 3,1 Bar     36.3 Watts
CRR: 0.01088
Rolling Resistance 35 psi / 2,4 Bar     38.0 Watts
CRR: 0.01139
Rolling Resistance 25 psi / 1,7 Bar     40.7 Watts
CRR: 0.01220 


As you can see, the effects of pressure on rolling resistance are surprisingly small (though I guess for a tire of this width 1.7 bar is already a relatively high pressure). Going from 45 psi to 55 psi for this tire saved only 0.7W per wheel when measured at a relatively high speed of 29km/h. At the same time you’d start to feel every tiny bump in the road and you’d have decreased grip on pebbles or debris.

I dimly recall an experiment where high pressures even started to increase rolling resistance on rough surfaces above a certain point.

As others have said in the comments, getting some good, slick (i.e. treadless) tires will improve rolling resistance much more.