I don't see why not; the quick-change periodization of P90X and Chalean Extreme is mostly there to prevent boredom. Bodybuilders (used in the broad sense, to include fitness and figure competitors) usually only change their strategy two or three times a year, or when they plateau. In an average year, they'll have a strength phase (like Burn), a muscle-building phase (Push), and one or more fat-burning contest preparation phases (Lean).
During a muscle-building phase, rest is important to allow for 100% effort on your heavy-lifting days. Taking an extra day of rest or light cross-training during the Push phase seems like a good idea. One thing I wouldn't recommend is going for a serious calorie burn on those non-lifting, non-running days. Recovery is an essential component of progress.
"Standing on the defensive indicates insufficient strength; attacking, a superabundance of strength." -- Sun Tzu
| current weight: 264.0