Hey misssmartypants (love the name)!

I think you can do 4x a week as long as you still allow yourself the rest day (like, Mon, Wed, Fri, Sun). But then your next week would look like Tues, Thur, Sat. The important thing during C25K is keeping that rest day to let your muscles do their thing before you go run again!

Congrats on getting started!

When I first started c25k, there were several times I thought I could just squeeze in one extra workout.  But, I read the info about the program which stressed NOT pushing faster or doing extra workouts so as not to injure yourself.  Since you're walking routinely, your fitness level is probably better than most of us couch potatoes, but all your muscles, tendons, and your joints need to gradually accustom themselves to this new activity.  One of the things I liked about the program was that it left me feeling like I could do more, and looking forward to my next chance to run.  I think that anticipation was a bit part of my success.  I'm registered for my first 5K in 2 weeks!

I was probably in the best shape of my life back when I lived in NYC, just because of all the walking I did.  I learned to walk really fast to get places, and my 4th floor walk-up helped too!  Of course, I was 22 then, which might have helped...

The general idea is to only increas the distance you go by no more than 10% a week. Do more and you are in greater danger of injury.

How most of the running workouts do it is first increasing the distance you go, then when when your ability to do distance gets better add a day. For example if you follow the C25k plan the way it is written then when you graduate you will be running 3 miles (or 30 minutes) three times a week. Here is one way you would take five weeks to safely transition to 4xday running.

W1   3    3     3

W2   3    4     3

W3   3    4     4

W4   4    4     4

W5   3    3     3    3

Another way would be to add an extra day, but cut back on distance. Again, considering starting after you have graduated from the C25k program:

W1   3   3   3

W2   2   2   2   3

And build from there.

Of course it depends on your goals and fitness levels. I am in the C25k program now (finished W5D3 yahoo!) and afterwards I am going to transition into a little more aggressive program because of the longer term goals I have for running and weight loss. I´ll have to monitor myself closely to make sure my body doesn´t overstress, but this is in part because I was a runner before and despite my weight my overall fitness level isn´t bad. Others who are finding the C25k to be more of a challenge might be better off doing as the program sponsors suggest, which is to level off for a couple of weeks to let your body adjust to the new activity level before you start taxing it again with increasing exercise. The best thing is to get to know your body and let it tell you what it can handle.

One thing I would recommend is getting a copy of either Bob Glover´s The Runners Handbook or the Competitive Runner´s Handbook. I first got them in 1984-ish when I got serious into running and I got the updated copies this year of both on my Kindle now and they are like old friends updated for modern technology. Both not only have great advice on nutrition and hydration, running strategy and sample training schedules, but they also do a wonderful job of explaining what goes into training so that you can become empowered to become your own trainer and design your own training regimine depending on your fitness and your goals.

Good luck.