The easiest way to do this would be for post-Ottoman demarcation of the Middle East, is much more based on religious and ethnic borders. Consequently you could have the following countries that are majority Shi’a of some variety:
An Alawite state in its lands
A Druze state in Palestine-Syria
Iraq (without the north)
Iran
Lebanon is divided between a Catholic and Shi’a majority states yet distinct from Alawite state nearby
Azerbaijan
Russian empire releases certain Caucasian lands under independent Shi’a domains
This would very easily double the number. A major issue, is that Shi’a are not particularly present in Africa, aside from Kenya and historical populaces in the Maghreb and Libya. Generally, Shi’a Islam did not spread to a large degree into sub-Saharan Africa and was extirpated in Northern Africa by the activities of Post-Fatimid Sunni states.
Egypt after the Fatimids was never ruled by Shi’a and Egypt had very few Shi’a communities. This leaves us with Shi’a Islam, generally having the character of existing in Asia and Europe. Shi'a communities historically and today common in the following areas:
1. Mazandran, since at least the 9th century. Originally a stronghold of Neo-Sassanid resistance, by the middle Abbasid period, it was a stronghold of Ismaili and Twelver Shi'ism. Historically, it was the site of powerful Shi'a states until the Mongol conquest under Hulegu. The Hashashin, ruling from the Zanjan directly south, commanded powerful confederates of Shi'a cities, communes and so forth, that defeated the Kwarezemshahs and resisting the Seljuq pressures. Later, the Ilkhans would convert to Shi'a Islam via this powerful Nizari-Twelver base in the Mazandran and newly Shi'a Turkic peoples in the regions north and west. This area no matter the circumstance, will remain Shi'a and is the vector by which the Safaviyya became Shi'a and subjugated Iran to Shi'a rule.
-Mazandran
-Parthia
-Fars
-Azerbayjan
-Media
-Yazd
-Hazara regions in Afghanistan
These derive their Shi'a islam via this Mazandran route
2. Shi'a's base within the Euphrates river valley. This area is the site of the oldest Shi'a communities, at Karbala, Najaf, Kufa and so forth. A place such as this, is the area with which all Shi'a islam radiated from and will remain such.
-Iraq
-Syria (Alawites and other Twelver)
-Alevi in Turkey
-Twelver in Lebanon
-Bektashi and other Shi'a in Albania
-Ghulat and other Shi'a in Bulgaria
-Twelver Shi'a within Sharjah in the UAE
-Modern al-Ahsa
3. Shi'a within the Indus River Valley and wider Hindustan constitute a large section of the Shi'a populace in the world today. Though in minority in every sector, either to Sunni or Hindus, their religion is nonetheless historically powerful in the region and in some areas of Pakistan dominates entire rural conglomerates. This community of Shi'a derive itself from the first recorded Shi'a states in the region during the 10th century. These Shi'a states in the Indus and Hindustan, were called Dawi (missionary) states by the Abbasid caliphate and the Ghaznavids. Their origin was through the Fatimid caliphate in Egypt, which sent forth various agents called Dawi to enter lands to the east and south with the intention of creating rebellions and creating Shi'a (Ismaili or Nizari) states in these regions that gave their loyalty to the Fatimid Caliphate. These Dawi states were extremely powerful in the Indus and other regions.
-Pakistan
-India
-Bangladesh
-Sri Lanka
-Kenya
4. Shi'a Islam within Yemen, a Zaydi region in Northern Yemen and parts of far southern Saudi Arabia. This area is unique for having a strong Zaydi contingent and for its relative lack of relation to the wider Shi'a populace of Twelver and Ismaili.
-Yemen
-parts of Saudi Arabia on border of Yemen
-Oman
-Zaydi within the wider Red Sea and Abyssinia
----
Extinct Shi'a areas of transmission
5. Libya-Fatimid Caliphate, that area which produced the Fatimid caliphate in the 9th-10th centuries. This area for reasons somewhat draped in shadows, produced a powerful Shi'a militant tribe in the region of Libya among the bedouin there. Here, we find that the area that was rural, was dominated by Khawarij and Shi'a militants, while cities and urban places were controlled by the general Sunni Arab populace. This status quo, is perhaps the fallout of the Berber Revolt, which brought within its fold a large number of Kharijite and Shi'a militant Arabs who opposed the Umayyad regime. Ultimately, this produced an extremely powerful Shi'a movement that would come to conquer Egypt, Tunisia, Sicily and expand itself through these Da'i states and rebellions. Its demise though, is mirrored with the fall of the Fatimid caliphate and decline under Ayyuib rule.
-Libya
-Egypt
-Indus Valley
-Druze
-Certain Is'maili groups in the al-Ahsa, yet not Bahrain
6. Shi'a within the Maghreb, liekly also derived from the Berber revolt of the 8th century, was extremely insular compared even to the Zaydi within Yemen. This is due to their distance and distinct practices and lack of Arab affiliation, them being a Berber conglomeration.
-Morocco
7. Within the Arabian peninsula was a growing Shi'a presence that stemmed from the resistance to Umayyad rule. These based first in Makkah, would spread outward to the Nejd and there fomented large scale revolts. One such sect, stands above the others. The Shumaytiyya which for a time dominated Bahrain, Al-Ahsa, were the progenitors of the Qarmatian and the origin of the Zanj Revolt to a degree. These are extinct today, the Shi'a within Bahrain and Ahsa today, are of the Twelver and derive from connections to Iran or Iraq.
-Historical Nejd
-Northern Iraq
-Southern Syria
-Oman
-Bahrain
-Historical Kuwait and Bedouin in Iraq
----------
You can work with these for a base^