The coupled cluster method (CCM) is a powerful and widely applied technique of modern-day quantum many-body theory. It has been used with great success in order to understand the properties of quantum magnets at zero temperature. This is due largely to the application of computational techniques that allow the method to be applied to high orders of approximation using localised approximation schemes, e.g., such as the LSUB
m scheme. In this article, the high-order CCM formalism for the ground and excited states of quantum magnetic systems are extended to those with spin quantum number
s≥21. Solution strategies for the ket- and bra-state equations are also considered. Aspects of extrapolation of CCM expectation values are discussed and future topics regarding extrapolations are presented.