Hey that sounds so off-the-wall that most people would likely dismiss it, but one chain could totally have mechanics providing for mining another one, theoretically.

I'm not up-to-speed on all the altcoin families out there; I know a handful of old ones.

As I mentioned earlier you could try to mine plotting coins like chia or expensive storage coins like sia with cheaper storage chains like filecoin, dunno how feasible that would be.

Many chains are proof-of-stake, meaning mining is the equivalent of holding coins.  Hence a trading bot for any of these, such as on an ethereum dex, could be thought of as similar to mining if it accumulates profit.

Some chains have AI components that can learn and predict things.  It might distantly be possible to break apart some of the mining algorithms involved, and use other chains to find ways to speed mining up, dunno.

The biggest return for the idea of mining one chain on another, aside from storage or other basic arbitrage, could be to create a chain that incentivises parts of the mining process of another.  For example if there is some kind of ASIC design challenge needed to mine bitcoin, you could make a blockchain that mines by solving that specific challenge better and better, and that blockchain would then hasten mining technology for bitcoin.

Why are ya asking?