The objective of this study is to identify the terms under which a national majority will
willingly include Muslim immigrants as full members of their societies on terms acceptable to both tparties. Our working hypothesis is that national majorities
are often willing to go farther to accommodate Muslim immigrants than has been appreciated, but are very sensitive to the terms of accommodation. We present results from a series of randomized experiments conducted on representative samples of the British public via the YouGov internet survey panel, in order to identify where the British majority draw the line between what forms of Muslim accommodation are, and are not, widely acceptable, and to illuminate which considerations majority members are sensitive to in deciding where to draw the line. Our experiments focus on concrete political and social issues, and include: examinations of majority views about accommodating Muslim religious practice in clothing choices and school food provision; accommodating separate Muslim schools; acceptance of Muslim political leadership in local government; and where free speech restrictions are appropriate to accommodate majority and minority sensitivities. By examining how majority responses in these concrete controversies are influenced by how they are framed, we will cast new light on the terms under which majorities in a multicultural society are willing to accommodate Muslim minorities.