Not only you can in theory, but also in practice I suspect both Gavin and Jeff would actually welcome multiple independent implementations of the protocol, since that's a good way for any potential vulnerabilities to be found and fixed.
And the other developers

I dislike the thread title, because I am but one of a herd of core devs under our lead dev, Gavin. It's either "Satoshi's client" or "the People's FOSS client" or "Gavin's client" or "Gavin/tcatm/sipa/BlueMat/jgarzik's client"........