Typically, yes, you can. Some notices of funding opportunities will specify an exact project period in Section Two: Award Information, e.g., Feasibility of Novel Diagnostics for TB in Endemic Countries (R01, Clinical Trial Not Allowed), but most set a maximum project period instead, e.g., NIH Research Project Grant (Parent R01, Clinical Trial Not Allowed).
Regardless of the length of the project period you propose, be sure to communicate in your application the reasoning behind the amount of time you expect to need to complete your project. Ultimately, the research scope of the proposed project should determine the project period.