We are running SDL Tridion Sites 9.1 and DXD services version 11.1.0-1054.
We are planning to containerize DXA for our environment.
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Should be possible. See, for example, https://blog.alexellis.io/run-iis-asp-net-on-windows-10-with-docker/
As of now DXA .NET 2.2 still not yet supported in .NET core and run-in containerize.