This fits about 10 once you take the cardboard insert out. I've used it for a few years and it has held up well.
I wouldn't focus on bringing your entire collection with you to places anyway. Pick 6-7 decks you think you'll play in a night and call it good. It increases the value you're out if you get it lost or stolen, and I only realistically expect to play about 4 different decks per night, so all 20 of mine would be overkill.
I cart my decks around in this. I have 12 of the ultrapro 100+ deck boxes I use for each deck, I took the insert out of this and can fit 12 of those deck boxes in here easy. Also has some pockets for a few random card that I wanna try in decks, and a large pocket for the few oversized commander cards I want to use.
I keep unfinished or unfavorite decks of mine in fat packs till I wanna rotate through them.
Ultra Pro Gaming Case with Red Trim https://www.amazon.com/dp/B0009F3DQ4/ref=cm_sw_r_cp_apa_aQlJzbKNFFXZA
That's what I've used for years!
Only complaint is it isn't modular, so if you have specific needs you'll have to figure something out.
I.e. I had to slice up the divider to fit my DS for Pokemon VGC events.
Outside of that, I could fit my 2 magic decks (one in the leather mana symbol one), ds, dice, and my Pokemon and yugioh decks, all in one go
I use this from ultra pro https://www.amazon.com/dp/B0009F3DQ4/ref=twister_B01N01UJSY?_encoding=UTF8&th=1
It comes with a foamboard insert, but I removed that and keep all my decks in the large Ultra pro 100 deck boxes, labeled for each commander. I can fit 12 of those in there which covers all my decks (wedge/shards and 2 random ones). With the insert, if you keep them in deck boxes you can get 12 in there, but the sizes of the slots in the insert are weird for EDH boxes, which is why I removed it.
I've had a bag like this for probably 10 years now and it hasn't failed me yet.
I have an older edition that only has 5 deck slots (the bottom middle one is for dice) and is a plastic divider, but I'd hope that the new cases are just as good.
One feature I like is that it has a bunch of slots in the lid where you can put individual cards or small groups that you want to have on hand. (Like tokens or sideboard cards.)
My buddy uses an Ultra Pro carrying case, each compartment holds a flip box perfectly, with some extra room in each compartment for tokens (maybe some dice).
It's not metal, but it's black, and you might be able to squeeze a binder in between the flap and the main area although that seems like it would compromise the zipper.
https://www.amazon.com/gp/product/B0009F3DQ4/ref=ppx_yo_dt_b_asin_title_o01_s00?ie=UTF8&psc=1
This is the case I use. It fits the original game plus the first expansion great. I had to take out the dividers to make everything fit. Really, I could fit everything from the 2nd expansion, the only downfall is putting your decks in deck boxes takes to much room and you're out of space. I see those board game bags that will work but for what i need right now I think it'll be to bulky and transporting the game will throw everything around inside of it unless you put other games in it which I wouldn't.
I've been in the camp of Ultra Pro Deck Boxes - the cheap $1-2 ones to hold 2 decks, but I recently discovered that these index card boxes at Dollar Tree can carry up to 3 decks with room for dice and tokens. Example - I need to get a couple more but my local store is out.
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Alternatively, Ultra Pro makes these cases. I can't speak to the quality of them now, but I still have one that I bought 12 years ago when I was playing Magic that still holds up.
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I use this https://www.amazon.com/Ultra-Pro-Gaming-Case-Trim/dp/B0009F3DQ4/ref=sr_1_1?s=toys-and-games&ie=UTF8&qid=1492880371&sr=1-1&keywords=ultra+pro+bag And I take out the insert and use these deck boxes https://www.amazon.com/ULTRA-Magic-Black-Green-Divider/dp/B00SVCASIS/ref=sr_1_3?s=toys-and-games&ie=UTF8&qid=1492880411&sr=1-3&keywords=ultra+pro+100+deck+box
I like this set up and can fit 12 decks in for when I go to our commander nights. I we do a thing where we roll a die to determine decks so I just roll my 12 sided and see what we get. It's kinda fun to do this, plus I have a wide variety to play that night and never feel like I am bored, and have plenty to lend out if a friend forgot their deck or something.
When I got to something more public I'll grab my leovold, my Marchesa, and something ultra janky, and throw it into my bag so that I can keep a better eye on things, and not worry about losing my collection basically.
This works great for me.
http://www.amazon.com/Ultra-Pro-Zippered-Gaming-Corrugated/dp/B0009F3DQ4
I removed the cardboard dividers and it holds 15 edh decks if you single sleeve and use the smallest box.
and a bunch of these http://www.amazon.com/Ultra-Pro-100-Black-Deck/dp/B0081IRWEU/ref=sr_1_1?ie=UTF8&qid=1458169556&sr=8-1&keywords=100+card+deck+box
I took the cardboard cut out of the bag and can fit 9 of those in there comfortably with room for tokens and dice and other essentials. While I like the other people suggestions that just isn't feasible for me anymore with the amount of decks I have.
This one - http://www.amazon.com/Ultra-Pro-Zippered-Gaming-Corrugated/dp/B0009F3DQ4 I actually have two - like it very much.
Would something like this work? http://www.amazon.com/Ultra-Pro-Zippered-Gaming-Corrugated/dp/B0009F3DQ4