You can sue for property damage. I don't think you have standing to sue to evict.
The above answer, and any follow up comments or emails is for informational purposes only and not meant as legal advice.
You yourself cannot start an eviction action but the cooperative could seek to terminate the proprietary lease of the owner of the shares associated with the unit, or the owner of the shares could seek to evict the tenant. It is incredibly difficult to evict someone for water leaks. Plumbing is a mystery to most non-plumbers, judges included, and if the tenant comes in and testifies that the leaks are arising in the plumbing, without any wrongdoing on his/her part, the court is likely to believe the tenant. I represent tenants, and in many cases like this , I was able to argue that the leak could not be tied to any wrongdoing on the tenants' part. The only such case that I lost was one where the building super testified that he retrieved corn cobs and bones that had been flushed down the toilet from my client's apartment. Without such a "smoking gun," it is very difficult to obtain an eviction based on leaks.
Dear New York Cooperator:
Your home owner insurance company's pressure on the cooperative's managing agent usually is enough inducement for the cooperative to direct the apartment owner's attention to the damage coming from the tenant occupied apartment. In the cooperative, the actual unit owner (not the tenant) is responsible for the damage and the leaks. That often is a compelling reason for the owner to investigate the cause and origin of the leaks and take action to abate the condition. The owner's plumber may conclude that the source of the water infiltration is plumbing which the cooperative is responsible to maintain. Or, the owner may discover that the tenant has a problem regulating water in a bathtub or sink. In any case, waiting two years to start to deal with this is a long time, and the cooperative's managing agent and board have had sufficient time to get to identify the cause of the leaks.
An apartment owner has no direct cause of action in a court against a tenant of another owner. The cooperative may deal with the apartment owner, but has no direct legal relationship with the owner's tenant. A proprietary lessee may take action against the owner of the offending apartment, but it would seem that if cause existed to do so, your insurance would have long ago dealt the other owner.
The time may be right for you now to secure your own attorney to help you determine the reason the leaks have persisted over two years and steer you to resolving the problem hopefully without need for a court proceeding.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.