During the Musaf prayer, the phrase "Mi Kamocha Ab Ha’rahaman" is replaced with "Mi Kamocha Ab Ha’rahamim." This custom is based on the Sha’ar Ha’kavanot.
The Sha’ar Ha’kavanot writes that there is a special Kavana (intention) that one should have during the Kedusha recitation in Musaf and Ne’ila on Yom Kippur, and one who has this intention can then ask G-d either for children who are righteous, Ru’ah Ha’kodesh (special spiritual insight), or wealth, and his request will be granted. While reciting the word "Ayeh," one should have in mind three dots underneath the "Yod," which in Gematria equal 30, and a "Kamas" vowel underneath the "Heh," which in Gematria equals 16 (the "Patah" equals 6, and the dot which extends from the "Patah" to form a "Kamas" equals 10). Thus, all the "Nekudot" underneath the letters have a combined Gematria of 46. This word is associated with the special "Shem Ayin Bet" – a Name of Hashem which combines the Name of Havaya ("Yod," "Heh," "Vav" and "Heh") which additional letters, and which has the Gematria of 72. The Gematria of the Name of "Havaya" is 26, and thus the additional letters have the Gematria of 46. One should have this in mind when reciting the word "Ayeh" in Kedusha during Musaf and Ne’ila on Yom Kippur, and then pray for one of the three blessings mentioned above. The Hazan should have this prayer in his mind, whereas others can actually verbalize the prayer.
During the "Aboda" section of the Musaf prayer on Yom Kippur, it is customary to bow on the floor when we read of how the Jews in the Bet Ha’mikdash would bow upon hearing the Kohen Gadol recite the Name of Hashem. The custom is that women do not bow, as this would be inappropriate.
There is a custom based on the teachings of Hacham Mordechai Sherabi (Yemen-Israel, 1908-1983) to sing on the night of Yom Kippur the "Ben Adama" hymn which was written by Rabbi Abraham Ibn Ezra (Spain, 1089-1167). This is a beautiful and powerful poem of Mussar, which speaks of the various stages of life, and warns us to introspect and not to be distracted by the vanities of this world – an especially appropriate message for Yom Kippur. Some have the practice of singing this poem after Musaf on Yom Kippur, but our synagogue follows the custom of Hacham Mordechai Sherabi to sing it after Arbit on the night of Yom Kippur.
Summary: The phrase "Mi Kamocha Ab Ha’rahaman" is substituted with "Mi Kamocha Ab Ha’rahamim" during Musaf on Yom Kippur. Although it is customary to bow on the floor at certain points during the "Aboda" section of the Musaf prayer, women should not bow. It is customary to sing the "Ben Adam" hymn on Yom Kippur; some synagogues sing this hymn after Arbit on the night of Yom Kippur, and others sing it after Musaf.