Abstract
A natural generalisation of lattice-lattice scaling is suggested which holds exactly for the second most singular amplitudes for the Ising model on the triangular, honeycomb, square and Kagome lattices. In general, this scaling theory requires three scaling parameters g, n and m, but includes extended lattice-lattice scaling as the special case of m=n. The generalised form of lattice-lattice scaling does not seem to be applicable to the three-dimensional Ising model. The connections between lattice-lattice scaling, its extension and generalisation, and the critical equation of state including correction terms are established and discussed.