If you have multiple contracts with a client on the same project and the type is different on each contract, e.g., one of the contracts has fixed billing while another is hourly, you can easily handle this using project phases. You can create multiple phases for the same project and set the Contract Type for each phase as required in Projects > General > Details. Each phase is a project in its own right and you can bill it as per its contract type. Check CORE Help Center for details on project phases and contract types.