  We provide a tensor calculus for $n$-number of ${\mathcal N}=(1,0)$ linear
multiplets in six dimensions. The coupling of linear multiplets is encoded in a
function ${\mathcal F}_{IJ}$ that is subject to certain constraints. We provide
various rigid and local supersymmetric models depending on the choice of the
function ${\mathcal F}_{IJ}$ and provide an interesting off-diagonal
superinvariant, which leads to an $R^2$ supergravity upon elimination of
auxiliary fields.
