  We generalise the expansion formulae of Musiker, Schiffler and Williams,
obtained for cluster algebras from orientable surfaces, to a larger class of
coefficients which we call principal laminations. In doing so, for any
quasi-cluster algebra from a non-orientable surface, we are able to obtain
expansion formulae for each cluster variable with respect to any initial
quasi-triangulation $T$, and any choice of principal lamination. Moreover,
generalising the `separation of additions' formula of Fomin and Zelevinsky, we
settle a conjecture of Lam and Pylyavskyy in the setting of quasi-cluster
algebras. Namely, we prove the positivity conjecture for quasi-cluster algebras
with respect to any choice of coefficients.
