The purpose of the question is to know whats out there. And if there isn’t anything, the second question is whether or not it’s an interesting idea. One of the downsides of 308 compared to 5.56 is that it’s heavier and has less capacity. But something I’ve been thinking about for a while, is why hasn’t there been a cartridge that kind of gives and takes from both cartridges. The idea is this would be chambered in an AR10 style rifle. But have the amount of capacity akin to an AR15 whilst also still being considerably lighter round per round than a 308. It doesn’t have to be exactly a 5.56 rim diameter, but something close. The qualities of the cartridge is that it would shoot flatter than 5.56 and 308, have more velocity than both as well as have more range than 5.56 and maybe 308 as well whilst staying supersonic. But probably be in between them in terms of ft lbs. Another added benefit is considerably less recoil than a 308. Is there anything that fits the bill, and if there isn’t, is it just a bad idea? The biggest potential issue I see here is in whether or not it could reliably fire in existing magazine designs without much modification, or preferably none at all.

Lots - designing other calibers to 308 and 223 cartridge base size/length is pretty common.

6.5 Creedmor
224 Valkyrie

6.5 creedmor uses a smaller diameter bullet, but the cartridge itself has the same rim diameter. And 224 Valkyrie is much of the same. I’m looking for something that has a case diameter similar to 5.56 but is as long as 308.

I can't seem to find any picture evidence at the moment, but I recall seeing a concept/experimental cartridge that did something similar to what you're asking but with the ar15/556. The cases were nearly straight wall in a small caliber allowing the standard ar15 magazine size to carry more ammo.

Ultimately I'm sure the juice wasn't worth the squeeze.

So you’re saying essentially an elongated 5.56, with similar COAL to that of .308?

Your question is a bit confusing because you keep talking about “rim diameter”, which had me thinking you were asking about a rebated rim cartridge the size of .308.

If I’m understanding you correctly, you’re talking about a cartridge with a case base/body diameter closer to that of 5.56.  Right?

I think he's asking about the .30 Super Carry concept,  but for rifles.

Gordon's Reloading Tool. Select .223 Rem and edit in cartridge designer.

5.6x50mm is the case you are looking for. It's a European case with the same head diameter as the 5.56; there is also a rimmed version.
Closest U.S. case is the 222 Magnum, which is 47mm long, and also the length of the 300 Savage/6.5 Creedmoor case, but has the same head diameter of the 5.56

Like 300 HAM'Rish? Longer?

You definitely are on the right track here. You’re understanding very well the principle of my question

I thought that there had to be something like this out there, thank you

I thought about describing it that way, but that’s pretty much exactly what I am talking about

I’m not an expert in terms of describing ammunition specs. So sorry about my lack of knowledge in terms of description. Yes, more or less correct

That’s really cool. Dang, it’s crazy to think that you would you would want even more 5.56 considering how relatively small it is.

Needs to be longer. And preferably using a smaller than 30 caliber bullet

You are asking about rebated rim cartridges like the .284.

I don't know any rifle cartridges that have a rebated rims down to .223 in a .308 class cartridge.

I'm not sure I get the question but Nosler has some designs with a rebated rim, 22 Nosler for example.  

There is also the 6mm Max.

What is the end goal?

Use the quote button under the post you’re responding to.  We have no idea who these responses are directed at without it.

That and you could've posted all that in one post............ I can't make sense of these fragmented comments.  

Or good job upping your post numbers.