You need to combine and make an overdrive monster to bypass the 999 cap. The way to do it is... Beat Official S tourney, then sometime after you'll be invited to the Icicle Festival in the second week of December. It's an A rank tourney, so by then it should be simple, beat that and you'll unlock a battle royal for every monster at various times of the year. The prizes for these battle royals is a Slate Fragment. A combination item that when used in combining results in the new monster being Overdrive.
Which means they have 1500 stat caps, but beware, they still have a total stat limit of 5994, the total if they had 999 in all six stats. So to raise a stat over 999 you'll need another stat to be lower to compensate. It makes you have to think about how you want to stat a monster. Strategize their stats. These are the competitive monsters, the ones for player battles.
Also, I'm not sure you need to beat S rank official to get invited to Icicle Festival, but that was about the time I was invited to it.
after u beat the big bang colliseum, there will be tournaments called battle royals and there will be one for each type of monster. after u beat one of these tournaments u get a slate fragment and with this u can combine monsters of that type to have overdrive which allows u to have 1500 max.
You can get the Icicle Festival invite as low as S-rank, I got mine immediately after winning the Official A cup. It might be possible to get it even lower.
After beating the Icicle Festival (which isn't that hard, it's much easier than the official S), Battle Royales for each monster type will show up on your calendar. Winning one of these will give you the slate fragment for that monster, use the slate fragment that matches your new monster when combining to gain overdrive status.
Be aware that some Battle Royales are rank SS and thus if you haven't won the official S you won't be able to participate in them yet. Also, even the Rank A Battle Royales are very difficult, be prepared.
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