Many symmetrically indivisible structures

A structure M in a first-order language L is indivisible if for every colouring of its universe M in two colours, there is a monochromatic M′⊆M such that M′≅M. Additionally, we say that M is symmetrically indivisible if M′ can be chosen to be symmetrically embedded in M (that is, every automorphism of M′ can be extended to an automorphism of M). In the following paper we give a general method for constructing new symmetrically indivisible structures out of existing ones. Using this method, we construct 2ℵ0 many non-isomorphic symmetrically indivisible countable structures in given (elementary) classes and answer negatively the following question from : Let M be a symmetrically indivisible structure in a language L. Let L0⊆L. Is M{up harpoon right}L0 symmetrically indivisible?.