The question is why are you so sore for so long? Generally, the answer is yes, you can train while sore. But there may be more to it than that. If you are suffering extreme soreness, then you are likely waiting too long between workouts of each bodypart, youre doing too much volume and blasting your muscles into oblivion, youre doing too much in the way of super-muscle-stretching exercises (usually isolation stuff, such as flyes that rip the muscle fibers) or, most likely, some combination of all these. If you wait too long to work each bodypart you suffer some level of detraining and then you get very sore. Many bodybuilders believe soreness=good workout. To some extent there may be some truth to this in that soreness is often a sign of new stimulusthat you did more than before. But, it could simply mean you trained, adapted, got sore/rested/detrained, trained etc... You may consider a bi-weekly routine (do each body part 2x a week) such as on a 4 day split. You can do a direct workout and an indirect workout for each bodypart. This eliminates doing many exercises and builds in a form of a heavy day and light day. For example, if you did back without direct biceps work, that would be your back/light biceps day. Then on another day do biceps, but include underhand chins/pulldown as one of your biceps exercises, this would also count as a light back exercise to make a light back workout. Legs can get tricky. You may end up just tacking on some 10-12 rep leg presses to one of your upperbody workouts to count it as a light leg day. Then, work legs by itself. Otherwise, just do something like upper body/lower body split. Oh yeah, cut back on the volume when you increase frequency. And, dont overwork you lower back like I did.