Logo Variations for Humor

I'm starting a website with a few buddies. We want to include a humorous section making fun of a popular social website, using a word that rhymes with the aforementioned site. It will be part of a much larger site, with the similarities between the two pretty much being the similarity in name and a few jabs at the site's function. Would I be able to make the logo similar enough to the actual website's so that the joke would be easier realized, or would that be copyright infringement? Afterall, it is a joke, and as far as I know you cannot copyright a joke. Thank you for your help!