I was thinking more in reference to the first BMB, where you could "hire" different minions and the shopkeepers had some items from the "black market" available (deadman's plate, lost chapter, pox arcana, etc)
If you think about how the game modes usually mix up the rift - mostly by adjusting the rules (all for 1, hexakill, poro king) or modifying a map (ascension, nexus siege, new dominion). There isn't much that leaves the rules and map the same, but allows the players to play it in a new and different way. BMB allowed the players to change things that players don't usually have control over (minions), and opened up some new items to make the rest of the gameplay interesting. In the end, the game itself was basically the same we play normally, but it felt new and fun because of all the different options.
By digging into that more, by adding the ability for players to interact with things like minions (what about being able to buy tower buffs?) and dishing up some new items or old retired ones or ones from other maps, the gameplay can be changed enough to be interesting, different and new. This does fall into the foreseeable trap that after a few weekends worth of play, the options are no longer new and exciting. This could be worked with by also using it as a testing ground for new items (like the did with Deadman's Plate and Lost Chapter) and/or introducing 1-3 new items each time it comes around. Eventually the items could be rotated, so each game has a different combination of randomly selected items (the Black Market stock isn't very stable). This helps keep builds from becoming stale, but does require additional items to pick from to ensure enough for every champ to feel good about.
Take the idea of a "black market" and run with it. What's out there in Runeterra that can be used, but isn't something that's easy to get? Even something as simple as old items - nothing mechanically broken, but what if Atma's was added back in for this? What if the shop keepers had some items from TT that they KNOW they aren't allowed to sell in SR but hey, it's on the Black Market? The options are there to take the game mode to the next level, and it would fill an area of the featured game modes that I don't think is filled by anything else.
Edit - by "mechanically broken" I mean mechanics that don't exist in the game anymore, like dodge