Can I be work on several project as a post-doc? I'm applying to a post-doc, with a specific project. I'm wondering how much freedom can I get as a post-doc.

I'm currently supervising a master student and I'm planning to supervise more during the post-doc. I'm also still collaborating with my PhD advisors and would like to do some extra analysis, on the side.

Having said that, I was wondering how much freedom do I get as a post-doc? I obviously need to work for the project I'm hired but I'm hoping to get some time to pursue other research interests and writing papers.

Would this be acceptable as a post-doc? Can I work on more than one project at a time?
It's quite common for postdocs to work on different projects at the same time, but this has to be agreed with the PI who is funding you. 

In my experience, there is a general understanding in academia that contracts are not strictly limited to the project being funded. For example, postdocs are often expected to apply for funding and this is rarely officially included in the scope of the project. Another very common case is publications: the potentially long process of publishing a paper sometimes overlaps with the next contract, but in general PIs are fine with letting you finish papers related to your previous contract.