  Given a holomorphic regularisation procedure (e.g. Riesz or dimensional
regularisation) on classical symbols, we define renormalised multiple integrals
of radial classical symbols with linear constraints. To do so, we first prove
the existence of meromorphic extensions of multiple integrals of holomorphic
perturbations ofradial symbols with linear constraints and then implement
either generalised evaluators or a Birkhoff factorisation. Renormalised
multiple integrals are covariant and factorise over independent sets of
constraints.
