The Everton Shareholders Association (EFCSA) have today released an online petition calling for "a vote of no confidence" in the club's board of directors.
And a fan group has urged owner Farhad Moshiri to "accelerate" changes to the hierarchy ahead of another Goodison Park protest.
The Blues are currently second from bottom in the Premier League, with just 15 points from 19 games. Once again the danger of relegation looms large after last season's late escape.
It has been a difficult January so far for Everton, with no new signings secured and three defeats suffered.
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An initial 'sit-in' protest took place after last weekend's 2-1 home defeat to Southampton - a game which Everton board members did not attend, with a club statement on the day of the match saying they had been advised of a “real and credible threat to their safety and security”.
Earlier this morning, supporter campaign NSNOW posted a new statement on social media which read: "Like all fans, we are appalled by the Everton board's recent statements & actions, including the use of unattributed leaks to the media, that have resulted in considerable damage to the good name of the club & especially the fans. For the board there is no recovery from this.
"Farhad Moshiri has to accelerate plans to replace the board with competent individuals. He must start this process immediately. As well as media activity this week, we will announce details of our plans for a further peaceful sit in after the Arsenal game #ALLTOGETHERNOW".
This afternoon, a tweet from the EFCSA account posted a link to a petition webpage with a message signed off by their 'executive committee'.
It read: "In our opinion our club continues to underachieve both on and off the pitch and the relationship the Owner and the Board have with the wider fan base is at an all time low.
"It is with great regret that the Association is asking fellow Shareholders and the wider fan base to sign our online petition calling for a vote of no confidence in the Board of Directors."
Today's developments come on the back of a particularly testing spell for the club, on and off the pitch.
After Everton went on the record on Saturday to state there had been incidents of “targeted physical aggression” at "recent home matches", various media outlets sought examples of these claims.
In response, club sources suggested chief executive Denise Barrett-Baxendale had been 'put in a headlock' on a matchday at Goodison, among other allegations.
Following further questions from the ECHO and elsewhere, it has since been confirmed that no formal complaint was made to Merseyside Police over the 'headlock' allegation - and it is understood that Everton now consider the matter to be resolved.
On Monday night, Everton said: “The club will not be making any comment related to specific historic incidents.”
The Blues are next in action away to West Ham United at 3pm on Saturday, before the home tie against Arsenal at 12.30pm on February 4th.
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