Avalon4 chips are and have been open for 3rd parties since release. Spondoolies often opens their chips up but availability is a bit behind actual release. I'd assume if you can put in a big enough order that Bitfury might consider taking your money as well, even Bitmain.
That's the thing though - Avalon's A3222 is readily available (A3233 slightly less so), but is the odd one out (in more ways than one). SP's is behind an NDA. BitFury used to be so accessible (even small group buys) that it spawned umpteendozen different miners, but now you'll have to show up with decent chunks of money. You'd know better about Bitmain, could you quantify 'big enough order' in their case?
Granted, that's based on what's available now and there might not be that much interest in current chips as it is - with people waiting for each developer's next chip instead (certainly for AM, the BE200 being lackluster); it's those chips' availability that I'm questioning.. as in, they're not available now, and there's very little indicating that they'd be readily available in the future.