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Can the subjunctive be used with "necessary" as in "It is not necessary that you (should) protest every time I say something." ?
Comments  
Yes, that is still common.
What is the difference in meaning between the following two sentences ?
1. It's necessary that he come to the party.
2. It's necessary that he comes to the party.
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The first properly uses the subjunctive.

Old fuddy-duddies will tell you the second is wrong. However, the subjunctive is fading from use, so I'm sure many people use it.
That sounds a bit formal (British?). I would likely say, "It's not necessary for you to protest ...."
Debpriya DeWhat is the difference in meaning between the following two sentences ?
1. It's necessary that he come to the party.
2. It's necessary that he comes to the party.
Here's how I hear the difference:

1. For some important reason, he has to come to some particular party that is going to be held in the future.
2. He always comes to the party (whatever party it may be), because it's necessary for him to do so.

Compare:

Mother says it's important that Johnny take his medicine.
(Johnny must take his medicine according to the proper schedule which extends into the future. Maybe something bad will happen if he doesn't, according to his mother.)
Mother says it's important that Johnny takes his medicine.
(Johnny always takes his medicine as required, and that's important. Maybe it's a significant step for Johnny to be taking on this responsibility, according to his mother.)
________

In both cases, the second sentence of the pair is a stretch. That is, it's less likely and maybe even awkward. Some speakers will find it meaningless; others will feel that has the same meaning as the first of the pair.

CJ
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Okay, I get it. Thanks, everyone.