Is it possible for a piece of cork to have more mass than a piece of rock?

Yes

Explanation:

It is entirely possible for a piece of cork to have more mass than a piece of rock. This would largely depend on the volume of the two objects. The density of a substance remains the same irrespective of the size of the substance.

                   Density = mass/volume

At constant density, it means that the mass of an object depends only on the volume of the object.

Hence, a piece of cork can weigh more than a piece of rock if the volume or size of the cork is bigger enough than that of the rock.