Yes, it is possible to change your MBA specialization at SPJIMR after the first year, but it is not a common occurrence. However, if you are looking to switch from Marketing to Finance, it is highly improbable but still possible to convince the management.
It's important to keep in mind that Finance is a specialization that requires a basic background in financial knowledge, which is not always the case for Marketing. This means that changing from Marketing to Finance may be harder for the management to accept than the other way around. It's also important to note that some students have been rejected when requesting to change their specialization.
If you have a financial background, it's possible that you initially tried to get into the finance specialization at SPJIMR but were accepted for your second preference of Marketing. If this is the case, it may be difficult to convince the management to switch your specialization in the second year. However, if you excel in finance subjects in the first year, it may be possible to convince them otherwise.