The biggest limitation is typically economics. Due to the large O&M cost of maintaining a nuclear plant, it is typically best to operate them at full power.
There may be other limitations based on the specific plant design. For example, in boiling water reactors, typically when operating at less than full power, there are changes to the MCPR penalties. As power decreases the MCPR penalties increase. This penalty is offset by the fact that you are operating at reduced power, however sometimes it may require a change to the control rod sequence in order to ensure that adequate margin to thermal limits remain.