During the final doxology my priest has the congregation sing, “Through him, with him, in him . . .” Is this permitted?
No. Only the priest is permitted to say those words, in Latin the Per Ipsum. Inaestimabile Donum says:
The assembly does not remain passive and inert; it unites itself to the priest in faith and silence and shows its concurrence by the various interventions provided for in the course of the Eucharistic Prayer: the responses to the Preface dialogue, the Sanctus, the acclamation after the Consecration, and the final Amen after the Per Ipsum. The Per Ipsum itself is reserved to the priest. This Amen especially should be emphasized by being sung, since it is the most important in the whole Mass. (§a.1.4, emphasis added)