Some compliment nouns are always plural, but other have singular forms - why?
Solution 1:
The word congratulate in the phrase "congratulate them" acts as a verb, not a noun.
As a verb, congratulates is not the plural of congratulate. The trailing "s" signifies singular agreement, and the form without a trailing "s" signifies plural agreement:
- Jack (singular) congratulates Jill.
- They (plural) congratulate each other.
Likewise for cheer and wish.