[ptero]

I would not do it on the sly.

Unless the company bosses are behind this idea you will need to overcome both legal problems and selling problems. For example, instead of buying your product the execs could fire you and hire someone else to do this internally. I see only three ways you might wing it:

1. Talk to your execs (ideally, the CEO) directly and sell this. On failure, be prepared to work on this internally. If so, ask for more money/promotion, which may not work but will not hurt either.

2. Call the other company and offer to improve their product for more money/promotion.

3. Get a techie friend to front for you: he approaches your company, you do the work, he shares the money. That's really grey area (being charitable). My 2c.