"through expanding" is a correct and usable phrase in written English.
You can use it to indicate an increase in size or scope. For example, "The company grew through expanding its product line."
– Staying faithful to a product vision through expanding releases.
She believes a big part of the success story come through expanding economic opportunities to women.
In Brazil, the challenge was overcome through expanding access to natural gas for cooking.
The special tapered structure could improve coupling efficiency through expanding the light receiving area.
Mr. Turner has larger hopes of bringing more jobs to the neighborhood through expanding the work of the school.
Typically, it has purchased financially struggling colleges and vocational schools and improved management while boosting profits through expanding enrollment.
The other part was Cordiant, composed mostly of Bates, which fell short in numerous attempts to grow through expanding business with existing clients or wooing new ones.
Sport, and specifically SFD, has been shown to facilitate positive outcomes such as social capital development through expanding networks and community building.
Through expanding this approach over the wider area, we aim at a fuller understanding of the human landscape interactions that have shaped the Stonehenge landscape.
Yang said he wants to "move in the direction of a single-payer system" either through expanding Medicare to everyone or creating a new system.
