The existence of colimits can be proved by adjoint functor type arguments: Lew Hardy and I wrote out details for the not too dissimilar situation of topological groupoids in ``Topological groupoids I: universal constructions'', {\em Math. Nachr.} 71 (1976) 273-286. Identification of vertices of a groupoid (or category) gives what Philip Higgins called a universal groupoid or category, and of course more compositions are allowed. Philip constructed this explicitly, but it also follows from the general construction. There is a mention of the cocompleteness of the multiple situation in (with P.J. HIGGINS), ``On the algebra of cubes'', {\em J. Pure Appl. Algebra} 21 (1981) 233-260. (see p. 238). Analysis and computation of colimits of various forms of multiple groupoids is necessary for applying Generalised Van Kampen Theorems - for the groupoid case this is most conveniently done in the `small' model of crossed complexes. For cat^n-groups (= n-fold categories in groups) it is probably most convenient to work in Ellis-Steiner's crossed n-cubes of groups (generalising Guin-Walery/Loday's crossed squares). Analysing pushouts of crossed squares led Loday and me to the non-abelian tensor product of groups (which act on each other). The identification of p-cells in an n-category (n>p) to give a new n-category is discussed in relation to homotopy theory in my survey ``Homotopy theory, and change of base for groupoids and multiple groupoids'', {\em Applied categorical structures}, 4 (1996) 175-193. That is, it shows how complicated and interesting are even simple cases of this general idea. We show how the n-adic Hurewicz theorem can be seen as an example of this in (with J.-L. LODAY), ``Homotopical excision, and Hurewicz theorems, for $n$-cubes of spaces'', {\em Proc. London Math. Soc.} (3) 54 (1987) 176-192. (This was the first proof of even a triadic Hurewicz theorem. The relative case goes back to early homotopy theory.) The general idea is of universally constructing an n-fold category from lower dimensional information, or lower dimensional identifications. The computational aspect (how to compute the answers) seems really interesting. One expects to be able to be more explicit in the groupoid case. On the other hand, even general double groupoids are a bit mysterious. Ronnie Brown