Laver indeed did it, not once but twice - as an amateur in 1962 and as a professional in 1969 - and fellow Australian Margaret Smith Court won all four Slams in 1970.
Graf, with her 1988 "golden slam" including Olympic singles glory, is the only other player in the open era to secure a same-year Grand Slam.
But having become the first woman since Jennifer Capriati in 2001 to complete the Australian Open-French Open double, Williams is now halfway towards pulling off the most extraordinary feat in tennis.
Take in the US Open she won last September and the world No 1 can hold all four Grand Slam trophies at once, as she did in 2003, if she lands a sixth title at London's SW19.
"I've got a Serena Slam and I'm close to another Serena Slam," said Williams.
"Wimbledon, the monkey's on my back because I haven't done well there in a couple of years."
Last year Williams suffered a distressing meltdown midway through a doubles match in which she was so badly affected by an apparent virus that she could barely hit the ball over the net.
The bizarre images of a dazed Serena stumbling around Court One - coming days after her lacklustre third-round loss in the singles to Alize Cornet - prompted some to start preparing her tennis obituary.
But the 33-year-old's response to the doom-sayers has been typically dramatic and decisive.
Having watched the ageless champion eclipse her 18 Grand Slam titles in Melbourne and then add a 19th at Roland Garros, fellow American Chris Evert believes Williams "has a great shot" at catching Graf's 22 majors this year in the most spectacular fashion imaginable.
"When she is at her best, she is better than anybody else," Evert said.
"To me, her game is better suited to the grass courts than it is to the clay."
Ominously, Williams believes she's getting better with age and says losses such as her fourth-round defeat at the hands of hard-hitting Sabine Lisicki in 2013 aren't as likely these days.
"I feel like I would win that match now," she said.
"Not because she's not a good player or anything but because I know how to win those matches now.
"So now if I get in a tough spot, I know how to win."
It is that unrivalled resilience which former world No 1 John McEnroe believes sets Williams apart from her challengers.
"To me, she's the greatest," McEnroe said.
"I've never seen someone come back from behind as much as she has.
"I can't believe she's got this will and belief at like really critical times. To maintain that belief is like a gift."
- AAP
