My current client and I have talked about going "full-time" and I've even discussed it with their legal department. The problem is they have a culture of standard employment contracts and are extremely uncomfortable with the idea of someone having a non-standard employment contract. They said it was "possible", but I'd have to list the projects to be excluded from their interests.
That precludes any opportunity to pursue any new ideas I would come up with.
That's just a flat out non-starter for me. I come up with new ideas all the time and I pursue or network those ideas all the time.
This is definitely a problem with my client and other large corporations. They understand that entrepreneurship is a growing interest of my many technical people and it has become a barrier to attracting those types of people. Something every corporation needs...people who think outside the box.
Of course the primary issue is leverage. If you need the company/paycheck and don't have enough of a background to command a change in the standard employment contract, then you have to sign away all rights. Or you can just decide to be a contractor and explicitly state (where it's necessary), that the work you're assigning rights to is in some amendment and is listed in detail. All other creations/works are yours.
Or you have a strong background with proven results and the corporation is interested in your services enough so that they will work with you on a non-standard employment contract.