How much can you train?

As much as you deserve to!

The factors involved in this:
Nutrition
Water
Sleep
Stress
Training goals
Training style
What do you want to improve at doing?
Are you after results or a workout?

Nutrition: If you are not eating well - don't ask me about over-training etc...Under-nutritioned does not = over-training.

Water: If you are not drinking enough water - don't ask me about over-training

Sleep: If you are not getting enough sleep - don't ask me about overtraining

Stress: Unless you live a charmed life and have no other stress (exercise is a stress BTW) - ie...job, girlfriend/boyfriend, husband/wife, family, etc...you must take your overall stress into account - Over-stressed does not = over-trained -
it ='s over-stressed.

Training goals: Your frequency of training will depend on your goals - do you have any?

Training style: If you are a hard charger - don't expect to train everyday - at least not at the same intensity.

What do you want to improve at doing?: Bodyweight pull-ups = daily, Weighted pull-ups = 3 or so days a week - define your goals.

Are you after results or a workout?: If you just want to beat the crap out of yourself and get a "workout" in - have at it but if you are concerned with adding to your 1 rep max, or another precise goal - focus on what you need to do to get results - not what you would do for a workout.

Just some thoughts on training frequency and over-training.

BTW - you can train yourself to handle almost any training protocol - if you approach it systematically and wisely.