It is the battery BMS that dictates the continuous current that can be suppled, it may be possible to replace the BMS with a higher continuous discharge one BUT you would need to know the exact cells used and the parallel configuration.
Likely the current BMS is optimised for the cells current rating so the answer would be no.
The controller current rating will be useful to know, it should be marked on the controller. It would be unwise to have a controller with more then 35a max current rating.
The battery BMS will also have an over current protection of more then 40a (possibly as much as 80- 100a), this though is only for a temporary over current for about 10 duration..