I would advise against it, your body needs sufficient rest and trying to rush it only increases your chances of getting injured. Given that C25k is meant to let you workout for only 30 minutes, I don't expect you're in great shape. This means you have even more risk of getting overuse injuries or other discomforts.
I think it would be better to stick to the plan and if you feel like it's going well, increase the loads (like moving to C210k halfway through) so you'll end up doing more each workout, but still getting enough rest. Normally 10 weeks should be sufficient to get finish the C210k program, which would allow you to workout for twice as long :-) If you think you can't do the C210k, just look @md5sum: you don't have to run fast in order to gain fitness!
To prevent injuries you could supplement your workouts with some basic strength exercises, like 2 sets squats, lunges and some other body-weight exercises. However, don't overdo yourself, running already causes enough strain to an untrained body.
Lastly, try to improve your live style. So take the stairs instead of an elevator, take your bike next time you need to do some quick shopping, take a stroll during lunch. Basically anything you can do to be less sedentary will aid you in gaining fitness.