Yes, the US has started five cases DS557 to DS561 for retaliatory tariffs imposed by Canada, China, the EU, Mexico, and Turkey All are at panel phase.
The request for consultations for all of these was passed to the WTO on July 16, 2018. For the first four cases, the panel was composed on 25 January 2019; for the last one on 28 February 2019.
I don't know this for sure from what the WTO has published so far about these 5 cases, but given the precedent the cases might be joined at some point, possibly during the appeal if that happens.