פירוש על ברכות 42:2

BEFORE THE PRAYER LEADER REACHES MODIM. One who walks into a synagogue and finds the congregation in middle of shmoneh esray, should only begin to say shmoneh esray if he can finish before the chazon reaches modim. And the reason that he should not begin unless he can finish before the chazon reaches modim is because he must bow for modim together with the congregation, so that it should not appear by his not bowing that he denies the G-d to whom the congregation is bowing. And the ruling is the same that he may begin sh’moneh esray if he will reach modim when the chazon reaches modim, since he will bow together with his neighbors. However the Gemara does not mention this because this situation that one may calculate that he is going to arrive at modim together with the congregation is not definite.
But it does not appear that because one who starts shmoneh esray who will not finish before the chazon reaches modim will not be able to say modim of the Rabanan is the reason that Rav Huno said this, for it is a mitzvoh to respond with modim of the Rabanan, however, it is not likely that this is the reason because we do not find any mention of it, modim of the Rabanan, in the Gemara. Since this prayer is not mentioned in the Gemara it is unlikely that one should not start saying shmoneh esray because he might miss this prayer.

Singer, p. 51, at which words the Congregation bows and makes a response.

In order to be able to make the necessary response.

Singer, p. 45, "We will sanctify," to which also the Congregation makes responses.