Belgian Goffin completed that trio, however, on Friday when he recovered from a sluggish start to thrash Dominic Thiem 6-4 6-1 and set up a daunting semi-final clash with six-times champion and overwhelming favourite Roger Federer.
It promises to be a momentous final week of the season for world number eight Goffin who this time next week will be shouldering Belgium's hopes of winning the Davis Cup for the first time in the final against France in Lille.
Before he can even start thinking about that he has to try to work out how to stop 19-times grand slam champion Federer on an indoor surface on which he appears almost unbeatable.
Goffin is 0-6 in previous meetings, most recently when he managed only three games in last month's Swiss Indoors as Federer charged towards an eighth title in Basel.
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"I've never found a key to beat Roger," the 26-year-old Goffin, who beat a hobbling world number one Rafa Nadal on Monday before being crushed by Dimitrov in his second round-robin match at London's O2 Arena, told reporters.
"Honestly, I don't know what to do tomorrow. But I'm going to try something, something different, something that I've never done in the past. I will try to do my best to play a better match than in Basel, for sure."
DIMITROV MAULING
Goffin appeared to be feeling the effects of his mauling by Dimitrov as he meekly went 3-0 down against Thiem on Friday.
But he suddenly came alive and won 15 points in a row to swing the match in his favour - breaking the error-strewn Austrian twice to take the opening set.
World number four Thiem looked flat, perhaps the effect of a 27-tournament season, and his game crumbled in the second set.
There was brief resistance in a 10-minute sixth game but Goffin held serve and claimed victory on his second match point with a searing backhand winner.
"As soon as I came back at 3-3 with a good service game, I knew that he was struggling a little bit with his groundstrokes," Goffin said. "He was hitting too hard maybe. He lost his timing, started to think about how to hit the ball."
Thiem, who qualified for the tournament for the second year thanks largely to a superb claycourt campaign, said he had just played a bad match.
"Too many errors, too many bad things. That's why I lost," the Austrian said.
The last time three players reached their first semi-final at the season-ending championships was in 2008 when Andy Murray, Novak Djokovic and Gilles Simon made it through.
Murray and Djokovic, together with regular qualifier Stan Wawrinka, were all absent with injuries this year.
Goffin will face Federer in Saturday's first semi-final before Bulgarian Dimitrov takes on Sock.
World number six Dimitrov crushed alternate Pablo Carreno Busta of Spain 6-1 6-1 on Friday for his third successive group victory.
Carreno Busta replaced fellow Spaniard Nadal who withdrew after his round-robin defeat by Goffin.
(Reporting by Martyn Herman,; Editing by Ed Osmond)
