In Smart Dispute application, we do not have any restrictions on submitting multiple partial chargebacks. on the same transaction. The users can modify the dispute amount and submit the chargebacks. The only check would be the cases would be listed as duplicates and users always have an option to move forward as it is not the duplicate.
In terms of scheme, MCOM does allow the above scenario of having multiple chargebacks active until total dispute amount does not exceed the transaction amount. However Visa has some restrictions in having 2 active cases at same time.