But Williams didn't back down from either challenge.
"Obviously it won't be easy", she said.
Pliskova had arrived in NY practically unknown except to tennis insiders when she beat Williams in the semifinals at Billie Jean King National Tennis Center in 2016. "She's had a lot of good wins in her career". "I hope that it's a little bit more comfortable on hard court, but I'm not sure".
"Just like I always say: Get your racket on it. Make a play on the ball".
Stephens could be headed for a semi-final meeting with Williams, although Williams acknowledged that in Pliskova she'll face a player with plenty of weapons in addition to her big serve. Williams continued with the almost flawless tennis she displayed in the third round against her sister Venus in Sunday's first set against Kanepi, the woman who upset the No. 1 player in the world, Simona Halep, on the first day of the tournament.
Kanepi, who had never previously taken a set off her opponent, was simply steam-rollered but she dug in with a break of the Williams serve at the start of the second set and settled into the match.
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The couple also told the newspaper they once gave Bobbitt $25,000 of the GoFundMe cash, and he spent it within two weeks. But then the story soured with accusations of mismanagement and outright theft of the money raised on Bobbitt's behalf.
Yet, Kanepi would have an answer in the second set with a 6-4 win to draw level.
There were more cheers when the home favorite then broke for a 2-0 lead and Williams rolled on to victory. Serena smacked a crosscourt backhand to break to 2-0 while Kanepi gained just four of the opening 18 points and failed to hit a single victor in the first set.
Seeded No.8 this fortnight, the Czech celebrated her 20th hardcourt win of the season and reached the last 8 for the sixth time in a major.
"Today [her serve] was unreturnable", Kanepi said.
"(Mertens) beat me two weeks ago so I knew that I had to come here and fight and do my best", Stephens said. "I heard that's an terrible thing to do". She hit 10 aces to Kanepi's 3, struck 31 winners to 14 and had 15 unforced errors to 12 to continue her bid to win the seventh US Open title. Doing it after motherhood would be all the more impressive. "If you beat Serena you feel like you can win any tournament you're in" Chanda Rubin said to BBC Radio.
It was about as flawless a start anyone could have to match Williams, who was guilty of just two unforced errors while firing 14 winners and converting all three break chances.
During the match, Serena defeated her sister Venus to secure a third-round victory. So I have some weapons, too.