ITA with everything aeh said - I'd pursue the neurospych eval. There's also something else I'd recommend, since the behaviors of concern are happening at home, but not happening consistently - keep a journal of when they happen, and include what your child was doing before they occur, where he is, what he's eaten recently, etc. It's possible that over time you'll find a pattern that either gives a clue to what's causing them or will at least give a clue to how to manage them.
I also wanted to add - I was primarily talking about my 2e ds above in my first reply, but now that you've mentioned the behaviors primarily happening at home I'll tell a little bit about my 2e dd. She's the ultimate tantrum kid - has meltdowns like you wouldn't believe, and that went on for years past the toddler typical meltdown years - at home. She's an angel in public - we get reports about what an amazingly well-behaved child she is *all* *the* *time*. Left dh and I wondering (often) if the person talking to us wasn't mistaking us for some other child's parents lol. The same dd was an academic star the first few years of elementary school, then her reading progress stalled out, first falling to grade level and then falling below grade level. We found out via an educational eval that she has a challenge with associative memory, and we eventually realized that her tantrums often happened at times when she appeared to have a memory glitch. The remarkable thing was, she continued to be able to hold it together at school and outside our home - but it wasn't for an admirable or good reason, it was because she was so caught up in not wanting anyone else in the world to realize she was struggling.
Best wishes,
polarbear
