Bumping Novak Djokovic off the World No. 1 singles ranking wouldn't just bring Andy Murray an elevation in his own personal status, it would also confirm that he and brother Jamie are truly one of the alpha tennis families.
They would have accomplished something that was beyond even the McEnroes. Never before, in the 43 years since the introduction of the official ATP rankings in 1973, has one brother held the No.1 ranking in singles and another brother reached the top line of the doubles power-list.
But after Jamie's accomplishment earlier this season -- he had an initial five-week run and then spent a further three weeks as the alpha-dog of doubles -- this family from Dunblane, United Kingdom, is poised to do just that. It's possible, depending on results at this week's Paris Masters, that Andy could be the No. 1 as soon as Monday morning.
A statistician from the ATP, who confirmed to ESPN that the Murrays would be the first brothers to do the top-ranking double, said that the family who had previously come closest were John and Patrick McEnroe. While John held the No. 1 position in both singles and doubles, Patrick's highest position was No. 3 in doubles.
Should Andy move past Djokovic, the Murrays would be bracketed with the truly elite families from tennis history.
With Arantxa Sanchez Vicario, who was the No. 1 for singles and doubles, and her brother Emilio Sanchez, a former doubles No. 1 (their brother Javier also wasn't a bad player either, and peaked in the top 10).
With Cara Black, a women's doubles No. 1, and her brother Byron, a men's doubles No. 1 (their brother Wayne climbed as high to No. 4, but he couldn't quite complete what would have been a family triple).
And with Serena and Venus Williams -- though of course no other tennis family will ever come close to replicating the achievements of the American sisters, who have each been the No. 1 for singles and doubles.
Serena and Venus have each spoken about how they wouldn't have accomplished so much if they hadn't had their sister with them on the tour, and before that on the practice court with their father. Though even the Williams aren't as close as the identical Bryans, who have been chest-bumping since they were in the womb, and who have what they call their "twin energy."
But don't discount how the bond between the Murrays has propelled them toward the top. What could have been more helpful for a young Andy during his childhood in Scotland, not a place previously known for its tennis culture, than having an older brother some 15 months his senior?
It made him into the competitive spirit he is now. On a more practical level, it also meant there was always someone around for him to play against at Dunblane's tennis club. As their mother Judy has said: "I think Andy has a lot to thank Jamie for. Jamie was just a bit older, and a bit better, and Andy was always striving to keep up."
More recently, Jamie has taken inspiration from his younger brother's achievements, and this year has put together the best season of his life, scoring his first two Grand Slam titles at the Australian and US Opens. Without Andy, Jamie wouldn't be the doubles player he is today.
More than anyone else in tennis, Patrick McEnroe knows how Jamie must have felt when he was going through some rough times in his own career. "When you're not doing well, and people want to talk to you about your brother, you just want to hide under a rock," the younger McEnroe once told ESPN.
"Of course, I was very proud of what my brother did, and he was a great help to me in my career. Jamie would probably say the same thing about Andy."
So history will be made if Andy can snaffle the No. 1 ranking and complete the family double, but there could yet be something even more special to come in the future.
Imagine if the Murray brothers could simultaneously be the World No. 1, with Andy and Jamie at the top of the singles and doubles lists.