It takes the same internals (some with minor modifications) as the MB-01 (L96), excluding the trigger unit.
So, to upgrade the barrel, you'll either need one specifically designed for the stock hop chamber. Look for Maruzen/APS-2/L96 barrels, these will fit, although they are about 5cm longer, meaning you'll either need a silencer to hide them, or you'll need to cut them slightly.
Or, you could upgrade the hop chamber to one that accepts AEG barrels. Depending on how much money you're willing to spend, you can get the PDI/LayLax chamber, or get a cheaper one from
here. If you get the one from here, you'll need the metal ring that adjusts the current hop-up, an AEG barrel and an AEG hop rubber.
If you have the Version 3 (with the velocity reducer in the cylinder head), then you will also need to upgrade the cylinder and cylinder head, as the stock one is too wide for the new hop chamber.
I'll check soon whether or not the MB-06 uses the same trigger upgrades as the MB-01 when I next get hold of my mate's rifle.