Thanks for providing the context around that period, to clarify was not imagining Mardavij himself was capable of achieving all his goals by himself had he avoided being assassinated (even with a Mardavij wank) rather ATL Mardavij would accomplish as much as he could in establishing the Ziyarid Empire with his successors continuing where he left off via an alliance with the Qarmatians, agree that it would be a tall order for Mardavij to take Baghdad.
You mentioned the Fatimids and Qarmatians could not even agree on the dissolution of the Abbasids in OTL, what if they managed to come to an agreement? Would the Fatimids have also been inclined to temporarily ally with Mardavij and the ATL Ziyarids? Were there other nearby groups from the north that would have been open to opportunistically go after the Abbasids in such a scenario?
From the north, there is only the Byzantines and their dependencies (that can harm the Abbasids, Kurds are very weak due to massacres of their stock during the Khawarij revolt in the north). Byzantium I find to be more favorable to the Abbasids than to Fatimids, Qarmatians or Ziyarid. I discussed this in a post regarding the Buyyid not long ago, about a possible Abbasid-Byzantine alliance. So no, for this period, the enemy for the Abbasids is not north and infact, their rescuer may come from there.
The issue with continued Fatimid-Qarmatians cooperation is that it is almost fundamental to Qarmatian thought. Fatimids were essentially a Shi'i state that attempted to overthrow the previous Caliphal authority, the Abbasids and establish a pan Islamic empire as the Abbasids did and Umayyad before them. It warred against the Abbasid to take its overall claim as well as for land. To accomplish this war of conquest and conversion (conversion as in, how the Islamic Uah transferred, converted to the Abbasid at the twilight of the Umayyad), the Fatimids employed a tactic of massive subversion and propaganda.
This led to the creation of dozens of heterodox Islamic groups across the Islamic world east of Syria and south of Palestine. Some of these formed into Da'i states that would be vassals of the Fatimids and receive orders from the central authority in Cairo from their Imam/Caliph. These Da'i states spread as Far East as the Gujarat in India and west as the Maghreb; a testament to the skilled subversion of the Fatimids.
One of the most fearsome of these Da'i states was the Qarmatians. Already existing as a small nucleus of fanatics in the deserts of al-Haasa, they existed as righteous followers and descendants of the Shumaytiyya (a militant Shi'i group that captured Madinah in the early 9th century, the followers worshipped their Imams), they were approached by Ali al-Dibaj (leader of the Zanj revolt) but rejected his claim to the Shumaytiyya and forced him out. This same group however, was then given new life with the subsequent Zanj revolt and Fatimid rise. Quickly, Fatimid benefactors they became and were tasked with fulfilling their duties as vassals of the Fatimids by crushing Abbasid power in Arabia and Iraq.
However, like with the Hashashin Nizari of Iran (Assassins), they began to run amok. The Qarmatians rejected the legitimacy of the Fatimid Imam claiming instead that the age of Islam (including the Fatimids radical shi'ism) was at an end. They imposed a new religious ideology that including a fanatical hatred of traditional forms of Islam, millennialism, reincarnation, communal society, rejection of authority, etc... Qarmatians thus began battling Fatimids and Abbasids across Arabia, Iraq and Syria.
It simply will not happen, Fatimid powers had given support to the wrong group and allowed them to grow and fester until that original fanatical anarchic nature prevalent in the Qarmatians overtook their allegiance to their suzerain. Regardless, the Abbasids defeated the rogue Qarmatians partly due to the blockades in the Sawad, indomitable Baghdad and their own skill of subversion. Qarmatians however, would last in some respects until the 18th century or longer.
So, the disagreement was that of vision. Qarmatians sought to dismantle the Islamic world (which means the Abbasid dominion, until 1300, Islamic world referred almost completely to the realm the Abbasids once held sway over) in the same manner as that or their predecessors of the 9th century; the Fatimid sought to replace the Abbasids with themselves as sole temporal and religious authority of the Islamic world. A difference in vision so great cannot be solved.