You can not directly control another faction's troops marching under their colors. You can however request to have troops lent to you. If your request is successful in getting your aligned faction to lend you troops, they will then have your factions nation crest displayed on them, and you can use them the same as you would your own, including putting your multi-national leader in command of them. If they lend you a stack of troops, you will get a message in the mail-box telling you so.
You can also use the <Tab> menu to 'paint' an area (one or more adjacent regions) you wish a specific faction to have greater (or lesser) interest in. That faction however will still decide how it manages that interest in this area.
One area per faction at a time, as far as I know.