  A multiplet calculus is presented for an arbitrary number n of N=2 tensor
supermultiplets. For rigid supersymmetry the known couplings are reproduced. In
the superconformal case the target spaces parametrized by the scalar fields are
cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant
potentials, subject to certain constraints. The coupling to conformal
supergravity enables the derivation of a large class of supergravity
Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing
the tensor fields into scalars leads to hypermultiplets with hyperkahler or
quaternion-Kahler target spaces with at least n abelian isometries. It is
demonstrated how to use the calculus for the construction of Lagrangians
containing higher-derivative couplings of tensor multiplets. For the
application of the c-map between vector and tensor supermultiplets to
Lagrangians with higher-order derivatives, an off-shell version of this map is
proposed. Various other implications of the results are discussed. As an
example an elegant derivation of the classification of 4-dimensional
quaternion-Kahler manifolds with two commuting isometries is given.
