It's true that 'between' can be followed by plurals, eg:
▶BETWEEN PEOPLE/COUNTRIES◀
relations [plural]
a) official connections between countries, companies, organizations etc
Relations between the two countries have improved recently.
however, ETS doesn't seem to like the idea. eg:
1. Dr. Sayre’s lecture recounted several little-known episodes in the relations between nations that illustrates what is wrong with alliances and treaties that do not have popular support.
(A) relations between nations that illustrates
(B) relation of one nation with another that illustrates
(C) relations between nations that illustrate
(D) relation of one nation with another and illustrate(B)
(E) relations of nations that illustrates
so just remember ETS' rule. no other way
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