How high can I increase the rent at a single time?
For a rental house in new jersey.
This all depends on whether or not you are under a lease agreement (instead of it being expired or a month-to-month rental).
If you are not under a lease (and its occupied), then you can increase it to whatever the market will tolerate, but give a 30 day notice. However, a typical increase is 5% (especially for existing tenants with whom you've had a decent relationship).
(Unoccupied) You can do whatever you want.
If you are under an active lease agreement, then you can't increase the rent (unless such an occurrence is specifically allowed in the lease).