Kapouleas and Yang have constructed, by gluing methods, sequences of
minimal embeddings in the round 3-sphere converging to the Clifford
torus counted with multiplicity 2. Each of their surfaces, which
they call doublings of the Clifford torus, resembles a pair of
coaxial tori connected by catenoidal tunnels and has symmetries
exchanging the two tori. I will describe an extension of their work
which yields doublings admitting no such symmetries as well as
examples incorporating an arbitrary (finite) number of tori, that
is Clifford torus triplings, quadruplings, and so on.