Haecceities and Haecceitism

Haecceities are primitive identities in a world. Haecceitism has to do with> primitive trans-world identities (allowing for de re differences between worlds without qualitative differences). My question regards the connection between the two. Prima facie, possession of haecceity implies haecceitistic differences between worlds. However, it has been pointed out that identity might be primitive with respect to a set of conditions but not others (Legenhausen (1989)), and showed that the two things can be kept distinct (Lewis (1986)), and in fact haecceitism can be true even if there are no haecceities. Adams (1979), one of the main recent proponents of primitive thisness, thinks haecceitism is also true, but feels compelled to provide an argument for it, additional to the existence of haecceities. Is counterpart theory the only way to believe in haecceities but not in haecceitism? Is it relevant whether haecceities are considered to be genuine properties (Duns Scotus), or just ‘aspects’ of things only separable via conceptual distinction (Ockham and other Scholastics, Adams himself)?
Generalising, it seems four possibilities are allowed; and if one introduces the distinction between moderate and extreme forms of haecceitism and/or anti-haecceitism (that is, as I understand it, primitive identity with or without essentialist constraints on the one hand, and non-primitive identity without or with the Identity of the Indiscernibles on the other) probably even more (8? I am not sure about extreme anti-haecceitism with primitive identities, maybe it only requires the Identity of the Indiscernibles to be a contingent truth). But which combinations are really possible/plausible? What conditions do they require exactly? What are people's intuitions/preferences?