Last season, Warriors overcame the challenge of Stormers, Munster and Bulls to claim the club's second league title.
Speaking to BBC Sport Scotland, Jones said: "It's a marker that you can lay down in your career and say 'we won the league, that was us, we were a great team', but it's something that we obviously now want to build on," Jones told .
"We don't want that to just be something we look back on as that one time we won the league, we want to build something big now.
"We would love to go on and win the league again. We'd love to go on a challenge in Europe as well. That'll be the plan moving forward, is that we become a great team."
Jones earned his 50th Scotland cap against Uruguay in July and he's hoping to replicate Warriors' success on the international stage.
"It would be an absolute dream come true if we were to win something with Scotland," the centre said.
"Obviously, you look mainly at the Six Nations, and that is something that we've played well in the last few years, but not well enough and not stringing together those big wins."
With the British and Irish Lions tour next year, Jones wants to put himself in the mix for selection, but knows a host of other players share the same aspiration.
"That is a huge personal dream and I'm sure a dream of pretty much every home nations player," he said.
"For me, that's all about staying fit, playing well. You've got to be in the conversation come the end of the season.
"I think everyone will be having that in the back of their minds at this point."