Moudim

Although it is quite common in recent generations to say it silently while the Tzibbur says Modim Derabonon, the Poskim were opposed to this and held it should be said out loud (saying there is no problem of Trei Kolei Lo Mishtam'ei since they are saying different things), as the original Minhag. And we find Rav Shimon Schwab also saying - "I don't know where did the Minhag of saying the beginning of Modim silently come from".

In KAYJ the Chazzan says it all out loud.

Michael FRBSH