Not going to happen, at least not before the note3 is so outdated you won't care. Samsung uses quality cells, no third party will be able to get more real capacity into the same size without a major advance in battery technology. And if that happens, it will be all over the site, you won't have to look for it. Anyone claiming more capacity in the same size is lying, period. If a manufacturer wants to challenge me on that, send me a battery and I'll test it. I have tested a bunch of them, and they all lie. Note that I'll be disassembling it, and testing it with real test gear. The sticker means nothing.
You can go thicker, zerolemon is probably the best choice for the money there. Extra battery, there are a few good third party ones out there. Or external. Or do wireless charging and set the phone on it often.
Personally, I like the extra weight and thickness of the zerolemon. The stock phone is too damn thin and slippery, and has less than half the battery life I want.
As for exploding batteries... Extremely rare. And the phone is partly at fault for improperly monitoring the charge. I've used el-cheapos from China and real OEM cells, and everything in between. Never a problem. I would recommend either OEM or a known good third party though. Just because they don't lie about capacity. I've even seen cells that are much smaller than claimed shimmed with plastic to make them the same size as stock. Ridiculous.