I don't think so because the effects of removing the rule would likely be a large number of people abusing it out of spite. Example: Party A takes Party B to court over something, and Party B is found innocent but Party A still believes in Party B's guilt, and repeatedly attempts to get them back into court, making Party B's life a living hell. That's an extreme example because I'm sure court costs would be a big deterrent, but I believe it happened often enough for double jeopardy to be instated in the first place.

The effect of keeping double jeopardy in place is that the prosecution knows they must take the time and effort to do whatever they can in order to build an airtight case, because they can't just call for a second trial if they don't get the ruling they were hoping for.

There are no exceptions especially explicitly stated in the US Constitution. Double Jeopardy should stand on its merit regardless whether tried twice for the same offense.

I think the Double Jeopardy law should stay. No one should be put to another trial for the same offense.

Even though there are some cases where it would be viable to take someone back to court on the same charges in example OJ Simpson.

However with this law no longer existent someone could try somebody out of spite on the same charges repeatedly. Making someone like that go through a bunch of bull shit that they have no control over.