Locally finite perturbation conjecture for edge-coloured complete graphs

Let $k\ge2$ be an integer, let $K$ be a finite clique, and let $c$ be a $k$-colouring of the edges of $K$ such that there is an edge of every colour. A locally finite perturbation of an edge-colouring is a colouring obtained by changing colours on the edges of a nonempty locally finite subgraph. Colouring perturbation conjecture. There is a colouring $\chi$ of the edges of the complete countably infinite graph such that every locally finite perturbation contains a copy of $K$ with colouring $c$. This extends the locally finite perturbation question to coloured structures and remains open.