How does merged mining actually work? I keep seeing people mention it but never fully understood the mechanics

I've been mining DOGE for a while but I'll be honest – I've been merge mining with Litecoin without fully understanding
how AuxPoW actually works under the hood.

I get the surface-level idea: same Scrypt hardware, same work, two rewards. But what I don't fully understand is how
the same block solution can be valid for two separate chains at the same time. Is the Dogecoin block essentially
embedded inside the Litecoin block? How does each chain independently verify it?

Also curious whether this architecture has any theoretical limits. Could you merge mine more than two chains at once
with the same hardware? Is there anything technically preventing a third chain from being added to the same mining
operation?

Would appreciate anyone who actually understands the cryptography breaking this down. I've read the dogecoin FAQ
but still have gaps.