I am interested in classifying Hopf or bialgebras up to cocycle deformation rather than up to isomorphism. For this, it seems natural to extend the framework to coquasi-bialgebras, the dual notion of quasi bialgebras due to Drinfeld. In terms of extensions, I will give some method of constructing coquasi-bialgebras and classifying them up to coquasi-isomorphism.