You total up all the modifiers for all PSR-inducing events (unless told otherwise in specific PSR triggers, such as one for firing a Heavy Gauss rifle after moving), and then roll a PSR at the final target number for each trigger. An extensive example is available in TW on page 61, explaining this.
In that example, a mech is kicked twice in the physical attack phase, losing a leg actuator, and taking over 20 damage: this results in the need of making four PSRs, two for kicks, one for destroyed actuator, and one from total damage suffered; all at a target of 9+ due to the combined modifiers from all the triggers.
So in your case you'd be making three PSRs at a combined modifier of +3 (+1 for each destroyed leg actuator, +1 for 20+ damage).