How possible is it for someone to grow taller at 22?

Not easily. There's a medical procedure that involves breaking each leg in 2 places, and stretching the gap between the breaks by 1mm each day (as the bone attempts to heal, it fills in the gap). You could grow 2 inches that way, but it's an extreme procedure. (Very painful, can't walk for about a year etc...) You'd have to be really desperate to do this.

A better bet would be go learn good posture. Slouching can lose you inches of height. You could also try shoe insoles, which will raise you height between 1/2 inch to 3/4 inch (which is worth it if you only want to be 2 inches taller).

If you're really desperate to actually grow, drastically increasing your calorie consumption may help you gain some height (after a year you could safely go back to your normal diet, since you will definitely have stopped growing by then). Adolescents who are slightly overweight for their age also tend to be (and end up) taller than their standard weight peers.

You should be aware that men finish growing 19-22 years old, whereas women finish growing early-mid teens (they usually stop growing at the same age they get their periods). So it's more difficult (more like impossible) to grow 2 inches at 22 years old if you're female than male.