Q:

No common CRS between two WMS service

I want to use two different data sources which I fetch from a WMS server, but they do not share any CRS.  For example, one of my data data sources comes in either EPSG 6706 or EPSG 4258, 25832, 25833, 25834 and Google Maps is not available in neither of these.  
Is there any way around it?  From everything I can read, it does not seem possible for QGIS (which is the software I'm using) to reproject on the fly data coming from a WMS, but I wish someone here faced this problem and eventually was able to solve it.  

A:

I eventually got it to work!  For some reason, I had to go in the Data Source Manager, in the WMS tab, then change the requested CRS there.  When I put it to ETRS89 (EPSG:4258) instead of RDN2008 (EPSG:6706), the data was shown at the right place.  
I really don't know where it was failing previously (QGIS not requesting the data properly or the target WMS not answering properly), but I'm glad to have it on track!