Of course! Also, as for the present subjunctive (which is even weirder in comparison), you use it in particular phrases about fear, worry, emotion, importance, etc. so that it follows “that” instead of if. You use it in all the cases you would use the past subjunctive, it seems, and for all verbs, too. For example, a common “subjunctive” sentence is “it is important that...”

For past tense, the sentence might be “it is important that he were nice when he was a kid,” which is awkward but fine for demonstration.

For present, though, you could technically say (and be correct in saying) “it is important that he be nice,” or “that I be nice,” etc. Or, for another verb, “it is important that he own a car,” as opposed to “he owns,” which is how we would normally say it.

Another wack phrasing would be “I want that he be happy,” or even “lest he be happy” would work.