1. If a person comes to start his Amidah when the congregation are already in the middle of the prayer, he should not start praying if he calculates that by doing so he will miss answering Kedushah, Kaddish or Barechu. Similarly, if it would mean that he would be unable to bow down at Modim with the congregation as he would be at a place in the prayer where he is forbidden to bow down. These rules apply even if by keeping them he will be unable to pray with a quorum. (Shulchan Aruch and Mishne Berurah 109)
2. Some say that he should not start the Amidah if this will cause him to miss saying Amen for Hakeil Hakadosh or Shome’a Tefillah. However, if he can time his praying so that his own saying of those blessings coincides with that of the cantor, he is allowed to start praying. (ibid)
