Multi-item multi-unit matching markets
I gave you an extremely vague lead in my other comment. Thinking about it a bit harder, I beieve you are right with having a look into the matching literature which I know a bit less.
Here is a setting that might be of interest: Kelso &amp; Crawford, Econometrica 1982.
They study $m$ workers (=buyers in your setting) and $n$ firms (=items), where a worker can only work at one firm, but a firm can hire many workers. Firms pay salaries to workers (=accept payments for a unit). If that is a setting that appeals to you, go straight to &quot;Matching with contracts&quot; by Hatfield &amp; Milgrom, AER 2005.