The Goulburn trainer nominated the Country Championships final in autumn as a goal for the four-year-old after he won the Highway Consolation (1400m) with ease on Saturday.
Williams said the Doncaster Mile could also be on the agenda provided Don't Give A Damn continues his form when he returns from a spell.
Don't Give A Damn, the $1.75 favourite, opened Everest Day with a 2-1/4 length win over Schedule ($21) after Kerrin McEvoy controlled the tempo throughout.
Super Star Bob ($15) was a long head back in third.
"He'll be aimed at the country championships and we could throw in a nom for the Doncaster if he was to improve," Williams said.
"He's a true miler or further, 1400 was just on the borderline of being a bit too sharp for him. He just had too much ability for the other horses.
- Chris Barclay AAP