Two flashes serving as fill will help here. You'll want to be familiar with the concept of "flash contribution". Sekonic (famous maker of light meters) do some webinars from time to time. Here's a link to a webinar that covers this topic:
Control the Light and Improve Your Photography: Part 2
If you skip to about the 30 minute mark and start watching, he shoots a subject in daylight where he varies the flash contribution.
"contribution" is the percentage of light provided by the flash as compared to the amount of light provided by ambient light. e.g. 30% flash contribution means that of all of the available light, 70% of it was provided via ambient light and 30% was provided via flash.
The reason this matters is because any light source will cast (or attempt to cast) a shadow. The sun will cast a VERY harsh shadow -- several stops of difference between the highlight side of a face and the shadow side. But by filling in with flash, that deep harsh shadow can become a soft gentle shadow -- possibly reducing the difference to just 1 stop (or maybe even less) of difference between highlight and shadow areas. If the flash contribution is more than 50% then the flash is putting out more light than the ambient light... at which point the flash will cast the shadows and the ambient light will behave as the fill.
You may find that 20-30% flash contribution eases the severity of the shadows and makes a more pleasant image.
You can have a different problem if you shoot in shade. Suppose you shoot in the shade of a tree, a gazebo, or a tent -- but you can see brightly lit background (e.g. the outdoors in full sun.) When the camera properly exposes for the indoor subject, the background will appear blown out. If you expose for the background, the subject will be severely underexposed. You need to match the subject lighting to the background lighting by using a flash even when you're in the shade in order to balance the image. You can't control the background lighting, but you CAN control the lighting in the immediately foreground with your flash.
Either way... if you're shooting outdoors, you NEED a couple of nice powerful flashes and know how to use them as fill.