Possible to do bodybuilding/ boxing/ martial arts?

I've been lifting weights for about 5 years now, and pretty built. I've boxed for a couple (mainly working the bag), and about a year ago started to go to boxing gyms. I've been doing martial arts (Jeen kune do) for about 6 months.
Now, my main goal is more of bodybuilding. Boxing, and martial arts are just something I love to do, I love the confidence it brings to know I can handle myself no matter who they are, and enjoy fighting. My current plan is first to get in to fitness modeling by at least next summer, and 2-3 years down the road I'm gonna start competing on stage for bodybuilding. As for normal jobs...Physichal therapy, massage therapy, personal training is all stuff I have in mind.

I've been having a ton of trouble doing all 3 though. First I was overtraining like hell, and gaining no weight. 6 days a week, sometimes I'd workout 2-3 times a day, and anywhere from 3 hours-5 hours in a days time. I said **** on that though, and cut it back to 5 days, and at the very most I workout twice in one day anywhere from 2-3 hours. I'm making much bigger gains now, and feel a lot better. It's very hard to do cuz I feel like I'm lazy since I don't do as much, but physichally feel 10x better.
Now, the thing is even though i cut back I still have some serious problems on the days I have to work, and then I'll go to the gym and lift, and then martial arts gym. So, I thought about changing my schedule to where I LIFT 4 days a week very hardcore, and I get each muscle done twice a week.
Day 1 I'll do legs, day 2 back/ arms, day 3 chest/ triceps/ shoulders, and then day 4 I will do my entire body, but more of cables and toning. Some cardio thrown in between on different days. Day 5 will mainly focus on martial arts. Of course I sometimes go 1-3 times a week so I'll have to change it up a bit, but do you guys think this is good???
I know boxing gets you tone which would help me with bodybuilding/ modeling, but it's hard when you want to get bigger, and if you didn't do all the boxing/ martial arts, and focused on weights you'd gain so much faster....Of course I'd be just another stiff, big guy with no skill, or speed. What's your guys input?

BTW: My diet is pretty good. I eat 6-8 meals a day. Mainly chicken, fish, tuna, eggs, fruit, and vegetables. Not many carbs. Take in a little protein with each meal. So, diet wise I'm doing enough to compensate for all the work I do.

 

Completely natural. The only supplements I even take are whey protein, creatine, and muscle milk. Honestly I don't react well to many drugs/ supplements anyways.
I know what you guys are saying about picking the most important, only one, etc. Doing all 3 I'm still making pretty good gains, but like I said if I'd focus on one my gains would be awesome...Especially after doing so much work, and cutting it down to only one thing to focus on.
I'm never going to box amatuers/ pro, and I'll probably never do a kickboxing tournament...Just something I enjoy. Guess I'll just try to do away with a little more of it, use that time to bodybuild, and see how I like it.

 

How long of workouts on those 3 days? I still box about everyday (even whenever I lift), but only do it for around 30 minutes. I mainly use it for tecnique though.

Alright, I'll post my new schedule here. I work abs everyday I workout, and most of my lifting takes me around an hour and a half-2 hours:

Day 1: I'll go to my martial arts class this day which takes around 2 hours. Earlier in the day I'll only do cardio (run, swim, jump rope, little bit of abs). NO LIFTING.
Day 2: Practice martial arts at the house (around 30 minutes), Lifting: Chest, triceps, and shoulders.
Day 3: Boxing- bagwork. Lifting: Legs. Do a little bit of swimming.
Day 4: Martial arts at the house, Lifting: Back, arms
Day 5: I made this a grueling lifting day. I work every muscle, but it's more toning...Around 10 reps per set. A lot of cables mainly, but also things like pushups, pullups, etc.

What do you guys think? That schedule covers everything except my martial arts classes are mon/ wed/ fri. I usually can only make it to 1-2, but if I can make more than 1 I have to fit it in there.
I'm practicing boxing/ martial arts everyday, but not overdoing it, working every muscle twice a week, and still getting pretty good cardio. Opinions/ suggestions?