Theoretically as many as you like - but probably not very many at the same time.
If you pass the credit check for one, you will probably pass for two, but then the systems start to get suspicious with all those credit checks and it starts to set off alarm bells of identity theft etc.
Over time though, there is probably no limit to how many contracts you can accumulate... though I'm not sure why you would want to!
P*ssing money right up the wall if they are not being used!