Hi Shaliesh,
Please try to understand the concept. You can assign and track the budget at Fund centre+ Commitment item level.
Now question is how you define your fund centres and commitment items. It depends on your business requirement. For your situation as described above, you can define your fund centre at the cost centre + contract level also. It means multiple fund centre for a single cost centre. You need to define derivation rules accordingly.
Through this you can assign and track budget project wise.
Regards,
Ankit K. Agarwal