  I prove a mass transference principle for general shapes, similar to a recent
result by H. Koivusalo and M. Rams. The proof relies on Vitali's covering lemma
and manipulations with Riesz energies.
  The main novelty is that it is proved that the obtained limsup-set belongs to
the classes of sets with large intersections, as defined by K. Falconer. This
has previously not been proved for as general shapes as in this paper.
