"support them on" is a correct and usable phrase in written English.
It can be used when you are encouraging or providing assistance or encouragement to a person or group of people to help them succeed. For example: "We need to make sure we support them on their journey to success."
We recognise that our trainers are individuals and bring different qualities, so we support them on a one-to-one basis, enabling them to use their own words and experiences to meet the needs of learners.
"PETA does lots of good for animals, but I could never support them on this".
Madonna and REM were big fans, the latter asking the band to support them on tour.
Instead, I went along to support them on the day they arrived.
He has two children, and for 15 years has been unable to support them on his salary.
Lechwes are unusual in having widely splayed, elongated hooves that support them on soft ground (e.g., sitatunga).
Amid cheers, Mrs. Obama, the third First Lady in the history of the university to speak at GW's Commencement, welcomed the students, acknowledged their families and loved ones who supported them on their journey in both known and unknown ways.
"I love Arsenal and I will be supporting them on Tuesday against Bayern Munich.
He has supported them on a number of occasions, including in 1996, when he voted to reduce tax windfalls for life insurance companies.
Supporting them on the night will be folk-rock group the Lumineers and Petty's longtime friend and former collaborator, Fleetwood Mac's Stevie Nicks.
The day when a critical mass of fans decides that the game is really an incubator of these problems, that it celebrated these transgressions, allowed and even supported them — on that day the game is irreversibly at fault.
