Originally Posted by slang

Resupplying Mir would be quite the challenge, it being burned up and all Resupply for ISS is done by carrying stuff on the Shuttle, and with unmanned freighters like Progress and ATV. I don't know how much cargo capacity Soyuz has, besides 3 astronauts. Progress was used with Mir too. Not sure if this is what you were looking for as answer, or maybe something more specific about consumables.