I know that OSM WMS service works with EPSG:4326 and EPSG:900913
I need to have an OSM base layer projected in another Projection, for example EPSG:32632
Do you know some way to do this?
Even Reproject WMS service, or download new tiles for Geoserver.
@Devdatta Tengshe gave the answer that works. Cascade the WMS service through another WMS that can do re-projection on-the-fly. It can be for example Geoserver, Mapserver or Mapproxy.
If you work with ArcGIS 10.x you can use 'Basemap' option: File > Add Data > Add Basemap > OSM. Than you right-click on Layers > Properties > Coordinate System and change to yours.
Hope it will help.