subjunctive after negative antecedent

[B.Joyia]

Does "suggest that" also demand a subjunctive in its negated form s.a. "not suggesting that" or "not trying to suggest that".

I know that the "circumvention" with should is very common and even accepted in linguistic circles in Great Britain,
and a google-search also indicates its very frequent use in common language in the US; - s.a. in:

"I am not trying to suggest (or "not suggesting") that every woman should necessarily have..."


However, in an attempt to write grammatically perfect US-English, would it have to be

"I am not trying to suggest (or "not suggesting") that every woman necessarily have...",

- or is the subjunctive superfluous and hypercorrecting here ?



Thank you for your help!

[fibbonnaci]

Subjunctive + that should always be followed by the base form of the verb( excluding 'to')

In, I am not trying to suggest (or "not suggesting") that every woman should necessarily have...

'Should' is the error. The second form you have written fits the grammar rules.
Though we are used to to mix 'should' with the subjunctive in our normal conversation, according to grammar it is considered an error.