Regularly done during the Syro Malabar Qurbana. The host is given to you by hand then you go and intinct yourself in the chalice. In other cases, some churches have a combined chalice and paten in which the priest/server will give you the host and you intinct into the wine or the priest/server will intinct for you and place it on the tongue.
I remember my first few experiences at Latin Mass were awkward because I would walk over with the host to intinct into the wine and the server would either give me a concerned look and let me intinct or they would cover the chalice and tell me eat the host first
. In my personal experience with other Syro Malabar Catholics at Latin Mass, I have noticed that many of us will skip the chalice entirely for this reason and only take the host. Drinking out of the chalice is just a very unfamiliar concept for some of us.