Automating Ethereum Address Generation and HD Key Derivation: Can One Private Key Yield Multiple Public Keys?

Question

I'm exploring methods to automate the generation of new Ethereum addresses for various purposes within my application. I'm particularly interested in whether it's possible to derive multiple public keys from a single private key in Ethereum.

Here are my specific queries:

Does Ethereum adhere to the concept where one private key corresponds to one public key, or is it possible to generate multiple public keys from a single private key? And i so how?

I've been investigating the Metamask API and its capabilities. Does the Metamask API provide functionality for generating new, unused Ethereum addresses? Specifically, I'm looking for an option to automatically generate a new Ethereum address, which, upon receiving funds, would transfer them to a predefined destination address.

Any insights, references to relevant documentation, or suggestions for alternative approaches would be greatly appreciated. Thank you!

I've conducted preliminary research to find an Ethereum wallet solution comparable to Electrum, which offers a convenient command-line interface for managing addresses and transactions. Specifically, I sought an equivalent to Electrum's "add_transaction" feature, which automates the generation of new and unused addresses.

As part of my exploration, I investigated the Metamask API but couldn't ascertain if it provides functionality similar to Electrum's "add_transaction." My goal is to automate the process of generating new Ethereum addresses, similar to how Electrum does it, potentially leveraging HD key derivation techniques.

To summarize:

I've researched Ethereum wallet options, focusing on features akin to Electrum's terminal commands. Specifically, I'm interested in automating address generation, similar to Electrum's "add_transaction" functionality. My inquiry revolves around whether Ethereum supports multiple public keys derived from a single private key, akin to Bitcoin's HD wallet capabilities. I'm seeking insights, advice, or alternative solutions to achieve this functionality within an Ethereum environment. Any assistance or guidance would be greatly appreciated. Thank you!