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Personally, I think that maximizing your VIP level at a single casino is the better choice, unless there is an excellent reward offered by other casinos, especially if you have already reached the maximum VIP level.
I agree with you about this, because the higher the level = higher reward we will get. But maybe having 3 different accounts in 3 different sites with the same level can be an advantage as well because maybe the rewards are different to each others. Of course to have these 3 accounts with good standing level requires a lot of money to spend. Only those who have big bankroll who can have 3 high level accounts in 3 different casinos.
It does take a lot of money to level up with 3 accounts on different sites and we might think that it's better to have 1 account and upgrade at a higher level.
But maybe the Op has another intention, namely to get a different advantage, as some people have said here.
But still, for me it's more fun to focus on one account and upgrade to a higher level and if that's achieved, you can level up other sites.
Because if this can be done I think the profit the Op will get will be even greater.