But the Jesuit who has been saying daily mass at my church is beginning to get on my nerves. Why? Because he invites everyone to say the doxology with him. For laymen, that's the "Through him, with him" part.

This isn't the first time I've seen a priest do this either-

The recitation or singing of the conclusion by the whole assembly is an extension that is unlawful not merely from a disciplinary point of view-as being against the rules now in force-but at a deeper level, namely, as being in conflict with the very nature of ministries and texts.

Even though someone could interpret this extension to the entire assembly as a sign of the desire of the assembly for increased participation in the liturgy, it is necessary that this desire be realized in an orderly and authentic way. What seems like progress is in fact retrogression: it is a sign of forgetting the part that belongs to each individual in the liturgical celebration. See SC art. 28: ". . .each person, minister or layperson, who has an office to perform, should do all, but only those parts which pertain to that office by the nature of the rite and the principles of liturgy." In the third case it happens often that the final is said or sung by no one or almost no one. If, on the contrary, the directions given in the Order of Mass (nos. 100, 108, 115, 124, "The people respond: ") are followed, it is possible in order to give greater emphasis to this response to use more elaborate chants that give force and solemnity to the acclamation of all the people (for example, the triple sung by all the people at a Mass celebrated by the pope or the more simple in the French missal of 1974, p. 103): Not 14 (1978) 304-305, no. 7.

The rest of the article has some good Q&A about procedural stuff involving the General Instruction of the Roman Missal (GIRM).

I have read that if one has a problem with a priest, to not criticize him and instead tell Jesus in his tabernacle, but I've got to do some research on the validity of that. In cases like this I would prefer to write a letter to the bishop rather than wait around for someone else to do something. Since the entire congregation is saying it, they obviouslly don't know it's illegal.