The latest show to face the boycott is by student dancers from Israel's Ben-Gurion University of the Negev who are to put on a show called La Karina on four dates next month at the St Brides Centre in the capital.
As the university gets funding from the Israeli government, there are calls to boycott the event in protest at Israel's military offensive in Gaza.
Last week, an open letter signed by more than 50 cultural figures, including Scotland's national poet Liz Lochhead, called for another show, The City by Incubator Theatre of Israel, to be axed by promoter Underbelly.
It is understood that the La Karina show is now also to be opposed. Advocates of the ban believe Israel tries to "lend itself a sense of cultural legitimacy and to distract attention from the brutality of its illegal occupation" through international trips by its artists.
Protests are now planned by members of the Gaza Emergency Co-ordinating Committee (Scotland) at the openings of the two shows, with hip-hop opera The City opening at the Underbelly Bristo Square venue on July 30, and La Karina to debut on August 9.
The promoter of the La Karina show, Stoneyport Associates, refused to comment on the boycott and demonstration. The dance troupe did not respond to emails from the Sunday Herald.
Underbelly said there was no change in its stance: "All artists, from whatever creed or nation, must have freedom of expression". Culture Secretary Fiona Hyslop has said she opposes "cultural boycotts".
Henry Maitles, a member of Scottish Jews for a Just Peace, said his group had come to the conclusion that cultural events backed by the Israeli state should be opposed, as they were designed to enhance the country's reputation abroad.
Maitles, a professor of education at the University of the West of Scotland, said: "In the light of the indiscriminate shelling and bombing of civilians in Gaza … combined with the internationally condemned illegal occupation and settlements in the West Bank and the illegal blockade on Gaza, we feel that nothing other than the strongest support for the isolation of Israel can begin to end the impasse." He said their stance was similar to boycotts which helped end apartheid in South Africa.
"Our aim is for a solution where people of all religions and none can live side by side in a democratic manner. Rights and justice for the Palestinians are central to this. Israel will need to be forced into this and the boycott is something we can push for to take this forward."
The ramping up of the boycott came as protesters throughout the UK took to the streets yesterday in protest at Israel's actions in Gaza. Several hundred took part in a protest in Edinburgh organised by the Scottish Palestine Solidarity Campaign. Some 45,000 gathered in London outside the Israeli embassy, after it was revcealed Israel's latest incursion into Gaza had killed over 1000 Palestinians, including at least 192 children.
A spokesman for the Edinburgh Festival Fringe Society said: "The Edinburgh Festival Fringe is an open-access festival. This means that anyone with a show can take part. No overall curator decides who can or can't take part, or what they should or shouldn't do. The Fringe Society neither selects or invites shows to take part and it is this founding principle of open-access that has led to the worldwide success of the event over the last six decades."
A spokesman for Ben-Gurion University of the Negev said: "The University is the embodiment of co-existence and has long been involved in many academic and research initiatives with Palestinians ... This involvement contradicts the claims of those who lead this inexplicable process against the university, a process which shows no awareness of the reality on the ground.
"A boycott of the university would harm efforts to strengthen co-existence and damage academic research collaborations for the good of all."