Where next?

[Johnbeddows]

I have been researching my Grandfather and his two brother and their service during WW1, I have had lots of info and photos on the two brothers Bertram and John Henry (his real name was Henry John), but I have not got much about my Grandfather who was the only one to survive. His name is John Beddows, DOB 2/10/1899 in Broseley Shropshire, but were living in Liverpool during WW1, his brothers N.O.K were in Garston, Liverpool. I know that he did serve as older family members remember a picture of the three brothers in uniform, which has sadly gone missing.
Any suggestions or info to where I go next in my search?
Regards John