The Scots are sitting second behind England in the table, and No.8 Beattie is upbeat ahead of the visit of Ireland on Sunday.
He said: "Everyone is in it, it's a very open championship, so there is absolutely no reason why not. The next challenge is very different with Ireland around the corner, but we are looking forward to taking it on and seeing how far we can go."
Meanwhile, Ireland could be without Cian Healy after the prop was cited for an apparent stamp on England's Dan Cole during the 12-6 defeat at the Aviva Stadium.
The 25-year-old will appear before an independent Six Nations disciplinary committee in London tomorrow.