It's hard to answer this since it's so dependent on tire and rim choice. Wider rims make effective tire size grow. Also tires almost never measure as advertised.
On your rims which are on the narrower side, you should be able to get most 25mm tires to fit. The 4000s typically measure 2-3mm wider than stated. Also remember that tire size grows 1mm or so after the tire sits on the rim for a few days.
I have an older SuperSix Evo which has similar-ish clearance and I'm stuck on 23mm tires on wide rims. The bike came with narrow rims and 25mm Schwalbe One tires which had enough clearance.