Multinational involvement in the SS started with the formation of 5th SS Division Wiking. It had volunteers from Denmark, Norway, Sweden, Finland, Estonia, later volunteers came from the Netherlands and Belgium under the command of German officers. In 1942, SS units were created using Croats, Ukrainians, Estonians, and Latvians. There were also SS units made up of Spanish, French, and even British POW's turned traitor, although the "Britsches Freikorps" was never more than a small number of members.
There is plenty of further information online.
WW2 Battlefield Relics: