Thank you Sybe:
One thing I need to have resolved first, otherwise anything I say from now on will not only be irrelevant but actually incorrect (based on a wrong assumption). Therefore I feel I cannot even comment when it comes to (Mara’s influence on) anagamis.
Up to now I have taken it that Mara can exercise his authority only in the Deva lokas and below, since he presides over the highest one of them (and therefore over the lower ones as well). If the influence of his power extended to even brahma realms, would his ‘seat of power’ not be based there instead? And how will he entice with forms and sense-pleasures those who have gone beyond them? This is only my thinking. I am not saying it is so, or even that it should be so. How is it in reality? I do not know.
Much metta