We describe asymptotic symmetries at spatial infinity of asymptotically flat spacetimes within the context of a generalization of the Beig-Schmidt-Ashtekar- Romano-framework. We demonstrate that it is possible to relax certain smoothness requirements of the asymptotic transformations considered previously, without violating asymptotic flatness. The leads to an enhancement of the asymptotic symmetry group that includes logarithmic supertranslations at spatial infinity. Our results compliment several recent results which confirm the existence of logarithmic supertranslations at spatial infinity in the Hamiltonian formalism.