OA is A.

my doubt is increase in option A indicate plural verb. But Subject "Intake of .." is sungular.. So I went for B.

increase there is infinitive and you should look at may... the construction is may+infinitive.

hope this help!!

Are you sure "may increase " is infinitive form of verb

a. Recent studies suggest that an intake of vitamin E in excess of that found naturally in a balanced diet may actually increase the risk of developing certain illnesses (CORRECT)

b. Recent studies suggest that taking vitamin E in excess of that found naturally in a balanced diet actually increases the risk of developing certain illnesses (Certain word-actually, whereas the original sentence contains UNCERTAIN word, "may". A sentence that makes a declaration of certainty does not convey the same meaning as one that allows for doubt...excert from mgmat SC chapter 1, pp17)

c. Certain illnesses may be at a higher risk of development if vitamin E is taken in excess of a balanced diet, according to recent studies (it's akward)

d. According to recent studies, the intake of vitamin E, if in excess of that found naturally in a balanced diet, may actually increase developing certain illnesses (...increase the RISK of developing, not increase developing)
e. Vitamin E, recent studies suggest, if in excess of that found naturally in a balanced diet, may actually increase the development risk of certain illnesses(suggest always bring "that" )

Recent studies suggest that an intake of vitamin E in excess of that found naturally in a balanced diet may actually increase the risk of developing certain illnesses, despite the claims of thousands of people who swear by it as a dietary supplement.

Mood of the sentence is Command Subjunctive.

subjunctive + that + bare form of verb
suggest + that + increase

suggest is command subjunctive verb. But, I cofused becuase the use of "may actually increase".

If the Option A does not have the word "may" then it seems to be correct.

Now, also compared to other options , A is correct.

Does "may increase" is a bare form of verb here?

Regards,
Karthi S