The ARP Church has followed the pattern of establishing a separate Synod in different countries which still work together. We have national synods in Mexico, Pakistan, and starting next year we are separating the North American into Canadian and US synods. We have never actually had a meeting of the different synods (e.g., something like a General Assembly with representatives of US, Mexico, Pakistan), but we cooperate and are in full fraternal relationships between the synods.
I was at our North American synod meeting this year about separating the Canadian presbytery into a separate Canadian synod. Most of the reasons given were practical. Some of the issues we've had to deal with lately (pastor's retirement, insurance, etc.) are completely separately handled by the Canadian presbytery. The issues they face in their country are different (this was quite stark during COVID where the largest number of our churches are in South Carolina which was in a very different political environment from our Canadian brethren). Travel is expensive and difficult. Also, the way our synod committees and meetings are designed means that every committee required representatives from the Canadian presbytery, which was relatively small, and often more distant not just geographically but from the issues being discussed.
The work in Canada started as a small effort as part of an existing presbytery (Presbytery of the Northeast[ern United States]), then its own presbytery, and now next year it will be its own synod. There were some similarities to the missions efforts in Mexico and Pakistan which led to them having their own synods.
There are disadvantages. We have grown more separate from our fellow synods in Mexico and Pakistan over time. Some of this is due to mistakes made, but it can be hard to maintain the same level of fraternity, even for churches just across a national border. We did have representatives from our Mexico and Pakistan synods speak this year, but I think this was the first time in a while we had from our Mexican brothers.
Somewhat regrettably, the reasons given during the discussion about separation were primarily practical and not theological. Recently the RPCNA similarly dismissed their Canadian churches to be a separate denomination. I shared this quote from
an RP article about the formation of the Reformed Presbyterian Church of Canada giving a theological justification for the separation on the floor of our Synod meeting:
God created the nations according to their languages, clans, lands, and the boundaries of their dwelling places (Gen. 10:5, 20, 31-32, Acts 17:26), and the Lord Jesus Christ commissioned His Church to make disciples of every nation (Matt. 28:19-20, Luke 24:45-47).
Our understanding is that the universal visible Church is distributed regionally among the nations of the earth. We note the prophetic promise in Isaiah 49:23, which states that kings shall be foster fathers and queens nursing mothers to the Church. And the Larger Catechism Q. #191 reminds us that when we pray “Your Kingdom come,” we are asking God to grant that the civil magistrates of every nation will maintain the Church within their lands.
I believe the RPs including the RPCNA have a "Global Alliance" to foster communication between the different national RP churches which may work a little better:
https://rpglobalalliance.org/