The England & Wales Cricket Board has vowed to take "relevant and appropriate action", after more questions were raised publicly about historical tweets from several England players.
Fast bowler Ollie Robinson has been ruled out of England's second test against New Zealand at Edgbaston, after historical tweets came to light last week when he made his test debut at Lord's.
The ECB is also investigating a second England cricketer for historical "offensive" social media posts, reports cricket website Wisden.com.
Wisden has uncovered a racist tweet, but chose not to disclose the identity of the player, because he was under 16 when it was posted.
Since then, tweets by other England players have come to light.
"Since we were alerted to offensive tweets last week, a number of historical social media posts by other individuals have been questioned publicly as well," says an ECB spokesperson.
"There is no place for discrimination in our sport, and we are committed to taking relevant and appropriate action where required.
"Given the concerns which have been raised are clearly now broader than a single case, the ECB board will discuss how we deal with issues over historical social media material in a timely and appropriate manner.
"Each case will be considered on an individual basis, looking at all the facts."
UK Prime Minister Boris Johnson has weighed in on Robinson's punishment, after Culture Secretary Olive Dowden described it as "over the top" for indiscretions "a decade old and written by a teenager".
England players have accepted Robinson's apology for the racist and sexist comments, says fast bowler James Anderson.
The 27-year-old Robinson apologised "unreservedly" in the dressing room for the 2012-13 tweets.
"The language and things talked about are obviously not acceptable," he adds. "He stood up in front of the group and apologised, and you could see how sincere he was and how upset he was.
"As a group, we appreciate that he's a different person now. He has done a lot of maturing and growing since then, and he's got the full support of the team."