Yes, there is a limit to how strongly magnetised an iron nail can get. This limit is called the saturation magnetisation, and it is the point at which the iron nail cannot be magnetised any further.

The saturation magnetisation of iron is about 1.6 teslas. This means that if you apply a magnetic field of 1.6 teslas to an iron nail, it will become as magnetised as it can possibly get. Any further increase in the magnetic field strength will not make the iron nail any more magnetised.

The saturation magnetisation of a material depends on its magnetic permeability and its magnetic susceptibility. The magnetic permeability of a material is a measure of how easily it can be magnetised, while the magnetic susceptibility of a material is a measure of how strongly it can be magnetised. Iron has a high magnetic permeability and a high magnetic susceptibility, which is why it can be so strongly magnetised.