So if we increased the magnitude of the magnetic field (e.g. by using an electric magnet), why couldn't we still have the sample float? Or does the Meissner eff

So if we increased the magnitude of the magnetic field (e.g. by using an electric magnet), why couldn't we still have the sample float? Or does the Meissner effect not relate to the magnitude of the magnetic flux? Unless, of course, the other end is attracting the magnet.