  Multivariate data occurs in a wide range of fields, with ever more flexible
model specifications being proposed, often within a multivariate generalised
linear mixed effects (MGLME) framework. In this article, we describe an
extended framework, encompassing multiple outcomes of any type, each of which
could be repeatedly measured (longitudinal), with any number of levels, and
with any number of random effects at each level. Many standard distributions
are described, as well as non-standard user-defined non-linear models. The
extension focuses on a complex linear predictor for each outcome model,
allowing sharing and linking between outcome models in an extremely flexible
way, either by linking random effects directly, or the expected value of one
outcome (or function of it) within the linear predictor of another. Non-linear
and time-dependent effects are also seamlessly incorporated to the linear
predictor through the use of splines or fractional polynomials. We further
propose level-specific random effect distributions and numerical integration
techniques to improve usability, relaxing the normally distributed random
effects assumption to allow multivariate $t$-distributed random effects. We
consider some special cases of the general framework, describing some new
models in the fields of clustered survival data, joint longitudinal-survival
models, and discuss various potential uses of the implementation. User
friendly, and easily extendable, software is provided.
