Let's take an example.
Providing $50k worth of LP on an ETH/USDC pair with an amplifier that has a 5% base APY and 15% max APY. Additionally, you hold $25k worth of Mute in your balance.
Amplified APY = 5% + ( (25k/50k) * (15% - (15%/3))) = 10%
To own the Max Amplified APY, you must hold the same value of Mute as you do of LP you are providing.
Your Mute holdings carry over to all amplifiers. If you are providing your LP to two amplifiers, your Mute balance is not split among them. Taking the previous example, if you provided LP on two pairs using those same exact numbers as above, your APY on both would be 10%. This is to encourage participation in the pools.