The phrase "and by supporting" is correct and usable in written English.
It can be used to indicate the act of providing assistance or endorsement in a particular context.
Example: "The organization aims to improve community health and by supporting local initiatives, they hope to make a significant impact."
Alternatives: "and by assisting" or "and through backing".
"And by supporting this project, you get to help save 2D animation from an untimely demise".
Only by forcing Putin to reverse aggression and by supporting Ukraine in this time of national crisis can we hope to restore peace in the region".
Education is not my top priority -- education is my top priority and by supporting this budget, you'll make it yours as well.
As a guaranteed purchaser of assets and by supporting the US economy in this way, the Fed gave confidence to other investors.
The Philippines angered China this year by accepting a gift of naval vessels from Japan and by supporting Japan's plans to strengthen its military.
He replied that his country has no interests in Iraq and by supporting the US it expects to be rewarded in trade relations and its own human rights difficulties.
Rather, impact investing could serve as a detector for the identification of highly innovative solution models for social problems developed by social enterprises, and by supporting them to increase and disseminate their impact".
With no real European institutions of democratic accountability — the European Parliament serves little more than a decorative function — the only way voters can express their dissatisfaction is by pushing to leave and by supporting extremist political movements.
Mr. Pataki has responded in kind with help for New York City's budget, and by supporting Mr. Bloomberg's bid for control of the city's schools, with equal parts of public praise for the mayor.
Actually, there were seven orphans who had come together and supported each other — my grandfather was one of them — and by supporting each other they ended up becoming a family.
"It's an amazing opportunity, a really fun place to work, and by supporting the scientists who look into important issues like climate change you'll feel like you're doing something really worthwhile".
