Increasing the stretchability of 100% cotton sofa fabric is a challenge because cotton is a natural fiber with limited inherent elasticity. However, there are a few ways to enhance the stretch to a certain degree:

Choose a Stretchable Weave: Some cotton fabrics are woven in a way that gives them more stretch compared to standard weaves. Look for cotton fabrics with a twill or sateen weave, as these tend to be more stretchable. Knit cotton fabrics, such as jersey knit, also have some natural stretch.

Select Cotton Blends: Consider using cotton fabric blends that combine cotton with elastane (also known as spandex) or other stretchy synthetic fibers. These blends provide significantly improved stretch and flexibility while retaining the comfort of cotton.

Use a Loose Fit Design: When upholstering your sofa, choose a loose-fit design. Loose covers can provide a bit more give and flexibility, making it easier to stretch the fabric over the frame.

Stretch the Fabric During Installation: When upholstering your sofa, work with a professional or follow best practices for stretching the fabric tightly over the frame. Proper stretching during installation can help you make the most of the fabric's inherent stretch.

Professional Assistance: Consult with a professional upholsterer or a textile expert who can help you find the right fabric, techniques, and tools to achieve the desired level of stretch for your project.

100% cotton fabric, even in the most stretchable forms, will never match the stretch and recovery capabilities of synthetic fabrics like spandex or elastane. If you need a significant amount of stretch in your sofa upholstery fabric, consider using fabric blends that incorporate elastic fibers, which are designed for such purposes. These blends offer both comfort and flexibility while maintaining the appearance of cotton.