The Sufi Mosque is the sole holy site representing Islam, and as a consequence, it is the most numerous minor faction and can be found on a massive number of maps. Since the site has only one unit that speaks a single language, this overuse makes them a poor fit on many maps. Splitting it into several new holy sites would allow more specificity for each site and a greater variety of representation overall. Islam has a lot more variation than just the Sufi orders.
The main branches of Islam could be represented by a Shia Madrasa and a Sunni Ribat and the Sufi Mosque could receive some alterations to accommodate this. However, so far there has been a tendency to choose only a facet of each religion rather than outright naming them after a major denomination (Bhakti instead of Hindu, Udasi instead of Sikh, etc), so alternate more generic names like Madhhab Madrasa, Ummah Ribat, or Mujahideen Ribat could be used instead of Sunni or Shia. More generic names would also have the advantage of being less limiting to what maps the sites could appear on.
For reference, the current Sufi Mosque has the Qizilbash as the unique unit, and the technologies, Fasting (+10% villager gather rate and -40% villager health), Pilgrimage (Ships one fattened goat for every 2 minutes of game length), and Sharia (+10 villager build limit).
A similar template could be followed for all of the Muslim holy sites with each having a technology that improves villagers and a technology that improves with game length. The sites could also provide a more in depth sample of the religion with all of the 5 Pillars of Islam (Faith, Prayer, Fasting, Almsgiving, and Pilgrimage) represented in some form by the available technologies.
Sufism is prevalent in Southeast Asia so originally the Sufi Mosque was geared towards that region with War Elephants as the unique unit and a selection of only eastern maps. This original emphasis should be retained, and the Sufi Mosque could be given a Southeast Asian unit and limited to maps in that region.
Moro Swordsman - The Moros are Filipino Muslims who fiercely resisted Spanish occupation. They would be armed with a machete and protected by a taming shield, buffalo horn armour, and plumed burgonet helmet. The function would be as an agile heavy infantry swordsman.
Fasting: +10% villager gather rate and -40% villager health.
Eid: Ships one fattened goat for every 2 minutes of game length. Renamed from Pilgrimage but otherwise the same effect.
Dhikr: Cards that deliver one-time troops and resource crates can be sent again (just like when advancing to age 5). It is a type of repetitive prayer, hence the repeat shipments.
Shi’ism is centered on Persia but is present as a minority across the Islamic world. Madrasas are essentially Islamic universities. Although madrasas are present in all Islamic traditions, it was initially popularized in Persia and their architecture often shows this origin with features like iwan. These holy sites could appear on most West and Central Asian maps. Since the Qizilbash were mainly Shia, this holy site could be their home. The featured technologies could focus on the study of religion, law, and architecture.
Qizilbash - Transferred from the old Sufi Mosque to this site. These were Turokoman warriors who would be a much better fit at a Shia holy site.
Hadiths: Ships a crate of books for every 2 minutes of game length.
Sharia: +10 villager build limit.
Minarets: Increases building LoS and build experience.
Sunnism is by far the most common branch of Islam so this holy site could feature on most of the maps where the Sufi Mosque is now. Ribats were fortifications built on the borderlands of Muslim nations as a base to raid and defend. Many were also repurposed as caravansaries along trade and pilgrimage routes and became religious retreats. The units and technologies of this holy site focus on the aspects of raiding and refuge these outposts provided.
Ghazi - This is a generic term for raiders across the Muslim world and they could feature as a cavalry unit similar to Raiders and Steppe Riders. The broad applicability and raiding focus is the perfect fit for a Sunni Ribat holy site. They actually already feature in the series as the Ghazi Raider in AoE4.
Almsgiving: +5% villager gather rate and +10% villager cost.
Pilgrimage: +10% speed for heroes, healers, and economic units.
Other major religions could also be split into multiple sites to provide fuller representation. Buddhism could be divided among the Zen Temple, Shaolin Monastery, and Forest Monastery. Christianity could be split among the Jesuit Mission, Hospitaller Commandery, and Papal Basilica.