Soundcloud – is there a workaround for remixes of known acts?

[Thousand Ways]

Soundcloud seems to have no problem with hosting anyone's unlicensed, royalty-ignoring cover versions of their favourite artists, and it hosts a lot of remixes that fans have made of their favourite bands. But whenever I try to upload my own remix of someone else's track, the site blocks it and sends me a warning. I can only assume that this disparity is caused by some known acts protecting their work more avidly than others. Is there any workaround for this? I'm not trying to make any money from the remix; I'm merely trying to have it heard.