Grow bags are OK for strawberries and other shallow rooted crops, as they are.
If you want to increase the depth of soil without incurring extra expense, then you can insert plant pots (with their bottoms removed), and infilled with compost, as shown below (the photo is not mine)...
The tomatoes in that photo could almost have been grown in the pots alone, as containers. Though having the grow bag as a base will help to stabilise the watering.
Alternatively, you could buy one grow bag, and use its contents to fill 3 large plastic plant pots.