How to approach spending token supply on liquidity pools?

Hello, let's imagine we have a new token we would like to initially deploy on BSC and Ethereum network. We will split the total supply of the token into half and put one half in the liquidity pool (LP) on BSC and the other half in the LP on Ethereum. Let's say, after a while, we will want to list the token on some centralized exchange (CEX).
My question is, where will we get some token supply to start a new LP on a CEX since we used up the whole supply when creating the two LPs on BSC and Ethereum? Should we take some liquidity out of the two LPs to be able to start a new one? Or we shouldn't have put the whole supply into the first two LPs and keep some tokens to be able to start another LP?
How do projects like Shiba Inu, BabyDoge and the rest of them approach expansion on new and new exchanges while keeping the same total supply?

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I have the same questions. I know a bridge can be used but I do not know if this is the way to do it or there are more alternatives. How the totalSupply knows what is in the pool in the other network otherwise?

On the other hand the bridge requires my token to be mintable and burnable to balance the supplies and I would like to avoid this.

I have tried to google this but I cannot find yet a proper answer.