The British team have only triumphed at the Tour de France (2012, 2013 & 2015), with second-place finishes in the Giro d'Italia and the Vuelta a España, by Rigoberto Uran (2013) and Chris Froome (2011 & 2014) respectively, their best results in the other two.
But with a host of new signings on board for the 2016 season, Brailsford hopes the team can challenge on all three fronts, as well as having high hopes for Classics success.
"Winning the big races intermittently is great, but ultimately, the challenge is to maintain that level of performance over a long period of time," Brailsford told skysports.com. "That is what we intend to do and that is what is driving us forward.
"At a preliminary stage, I don't see why we can't go for all three Grand Tours and have a real good crack at that. It's very premature, but that would certainly be something that looks attractive next year.
"We still want a Monument. We have got to put a lot of thought and effort into that next year, for sure."
With Mikel Landa joining from Astana, Sky have a young but experienced rider in place to tackle the Giro d'Italia next May. The Spaniard finished third and won two stages at the 2015 edition, all while playing second fiddle to Fabio Aru.
The 25-year-old could also double up to take on the Vuelta in the autumn, but Sky have an embarrassment of riches in their stage racing paddock, with Geraint Thomas likely to prioritise the multi-day events next year and could be one to lead at a Grand Tour.
With Sergio Henao returning to his best following a serious knee injury, and super domestiques in the shape of Leopold Koenig, Mikel Nieve and Beñat Intxausti, Sky's potential Giro squad has never looked stronger.
If Sky are to win one of the five one-day Monuments - something that has eluded them in their six-year history, new boy Michal Kwiatkowski is their best bet, having shown his Ardennes Classics credentials with his Amstel Gold Race win in April.
In the cobbled Classics, Thomas would be the team's strongest chance of immediate success, although Luke Rowe is proving himself to be a rising star over the pavé, with his eighth-place finish at Paris-Roubaix this season.
Brailsford is not the only team boss to be targetting a clean sweep next season, with Tinkoff-Saxo owner Oleg Tinkov claiming Alberto Contador and Rafal Majka could win all three Grand Tours between them.
The gauntlet has well and truly been thrown down.
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