Scarlets wing Ellis Mee could see his starting place could be in danger, with Josh Adams also having started the defeats by England and France.
Dragons co-captain Carter is in line to replace Montpellier lock Adam Beard, who produced a glaring error during the 54-12 defeat by France.
Beard tried to put a kick through but it resulted in a try for France fly-half Matthieu Jalibert with television pictures showing Tandy reacting angrily in the Principality Stadium.
Carter, who came off the bench against England and France, has won 16 caps but has never started a Six Nations fixture.
Scarlets back rower Plumtree could come in at the expense of Olly Cracknell, with the in-form Aaron Wainwright potentially moving back to his preferred position at number eight.
Wales have lost 23 out of the previous 25 internationals and suffered 13 successive Six Nations defeats. The past home win in the tournament in Cardiff was against Scotland in February 2022.
Scotland, who also name the team on Thursday, arrive in Cardiff having defeated England 31-20 in Edinburgh.
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