To just add to BR's input. I believe the thinking behind his recommendation to keep the off days is to stimulate growth in as little workouts as possible, that way you stimulate growth, yet have the extra calories from the days off to help with the calories needed for repair/growth.
If your main goal is fat loss - i personally am a fan of training/exercising as often as recovery allows. But i would do cardio on the off days too.. i am a firm believer that one can train every day or 6 days of 7 for a set amount of time (if planned de-loading periods are implemented) - i believe that the theory that one can't train everyday came from the misconstrued point that a muscle needs 72hrs to recover.
Firstly this is generally applicable to a new trainee - but secondly, with training splits for the resisted training ensuring no same muscle is over trained in 2-3 days, and with a nice vareity of (generally very repetitive) cardio-vascular work there should be little issue training a good 6 days a week.
So if you do 2 on, 1 off for the weights - which IME is plenty of a highly trained and chemically assisted person - then you could do cardio on the days you train - either post workout or preferably at a dfifferent time of the day, and also add some cardio to 2 off days. This can be lower intensity, in fact i would plan for the 6 different cardio sessions per week to be different exercises, and different intensities.. keeping the weights as intense as possible to make the best use of the anabolism and the 'delayed' calorie burining effect from intense exercise.
This is what i would do - and what i would advise a fit and experienced trainee to do.