For example, “flammable” and “inflammable” both describe an object that can easily catch on fire. I can also think of “ceased” and “deceased”, both of which can mean someone or something has been brought to an end.
edit: Some people are including words that can also mean its opposite (like sanction or table), those are cool too! The more weird words, the better!
I find intensifying to be more natural than negating for things like “I couldn’t care less,” or “irregardless,” or “misunderestimate” to a certain extent — if something is “worthwhile regardless,” I don’t have to regard that, but if it is “worthwhile irregardless,” I really don’t have to think about it at all. It just seems right that if I put a bunch of negative words in one sentence, it should be really, really negative, instead of it being negative if I used an odd number and positive if I used an even number; same with prefixes and suffixes. I think it’s probably too much to try to reform English to work as such, but if I were building a conlang it’s what I would do.