Abstract: For a manifold W and an E_d-algebra A, the factorisation homology of W with coefficients in A admits an action by the diffeomorphism group of W and we consider its homotopy quotient W[A]. For W_{g,1}=D^{2n}#(\#^g S^n×S^n), the collection of all W_{g,1}[A] is a monoid by taking boundary-connected sums. We discuss its homological stability and describe its group-completion in terms of a tangential Thom spectrum and the iterated bar construction of A. We do so by identifying the above collection with an algebra over the generalised surface operad, establishing a splitting result for such algebras, and studying the free infinite loop space over a given (framed) E_d-algebra.