By-product and Nth-product

By-products is a secondary product derived from a production process of primary product.

Is there anything like tri-product, four, five .. Nth?

Thank you.

The term By is originally an adverbial particle of place, meaning proximity, nearness. [etymonline.com]

So being a byproduct refers more to it being a minor result or side effect of the process rather than the major, primary result.

Spelled differently the term Bi indicates two or twice of a thing. Bi and tri- can enumerate things reaching the Nth item in general. These are not used to precede Product to describe the various elements of a process.