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We could try to filter the WPLANG option locale (see e.g. this approach by @brasofilo or this one by @toscho ):

is_admin() && add_filter( 'locale', function( $locale )
{
    if( $lang = get_user_meta( get_current_user_id(), 'wpse_lang', true ) )
        $locale= $lang;
    return $locale; 
} );    

where we check if the current user has the wpse_lang user meta key set, with values like is_IS, da_DK, ...

Then we could add the language selection for each user, on the user settings page.

There we could use the wp_dropdown_languages() function, with the get_available_languages() function, to display the select-box for available languages.