I attached a quickly smashed together light setup.
You will have 2 large soft boxes (diffused) as main light and fill.
And in the background 2 strip soft boxes (diffused, no grid) with overlapping lights on the background to eliminate the shadows.
For both fill and key: Bigger softbox is better in this case, as the light wrapping around is helping to minimize shadow.
The fill is better placed as much away as possible (and your room and strobe allows) as this would even out the light.
Placing the lights might get a bit finicky as you want to keep the light off the model, overlap them so, that you are getting no gradients and have them just so bright that the background just touches the pure white brightness.
If you go overboard with the brightness on the background you will lose considerable contrast in the image due to flaring. With that many lights and not much brightness difference on the model, the image will quickly look a bit flat. You somewhat have that in your example image as well.
Also you might nee to play around with the placement and distance of the fill to get the area in front of the model bright enough without flattening the image too much. You might even want to consider another strip box in front down on the area in front of the model just for that purpose.
Alternative: Background light from behind
An alternative route would be to use a huge piece diffusion fabric and use the 2 strip boxes from behind. This would make placing the strip boxes easier.
Alternative: Fill from above
If you have a huge fill from above, you could also make due with a lot less lights, but usually people do not have studios with a ceiling that high at the hands.
If you have a white ceiling, you could also try bouncing one light up there to see if you can use that instead of the fill.