How many isotopes can an element have?

There is no fixed number to which the elements are restricted to have.

Some have only two. Others can have three or even four

The element with the greatest number of known stable isotopes is tin, with 10 stable isotopes. Including unstable isotopes, mercury, cesium, and barium are each known to have 40 isotopes. Theory predicts however that many unstable isotopes should exist which have not yet been discovered (especially on the neutron-rich side of the line of stability.)