Great question — answering as the UphillTech team:
Yes, that's very possible; you just have to make sure that at least one Dimension differs between all the affiliates. For example, you could have Medium set to 'affiliate' but use the Source to differentiate between them. Or, if you want to keep the medium as 'referral' or similar, and to use the Source 'affiliate' then instead you could use the Campaign field to differentiate between them. Finally, if you want to use all three of these fields for your own purposes, you can use a Custom Dimension to differentiate between them, but that would be a whole lot more complicated.
Full answer by J Brazier: https://webmasters.stackexchange.com/a/106824 (CC BY-SA 3.0).
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