What I'd like to see in EUIV:
Religion
Eastern Orthodox & Oriental Orthodox relations should be closer, whereas the relations between Eastern Orthodox & Roman Catholic should be worse (or about the same). The reason for this is that Eastern & Oriental Orthodox are, when it comes to theology & even practice, the closest of all the Christian groups usually in game. Also, due to being under the control of the Muslims, their relations were also closer due to both being persecuted and both being under the same occupation.
On the other hand, Eastern Orthodox & Roman Catholic relations after 1204 should be bad, and not just a little. This is due to the real theological differences, but most especially due to the 4th Crusade. While the Sack of Constantinople wasn't done with the approval of the Pope, this didn't matter to the Eastern Orthodox people, who projected the action onto the entire Roman Catholic Church, and any really good relations which had existed prior to that event effectively were permanently severed.
Christian Councils
One of the most important things I would like to see added though, is the ability to "mend schism" through councils. In EU3 and other series, sadly, the only real way to "Restore the Pentarchy" is to do it through military conquest. However, I'd like to see decisions which allow you to call for councils between your Christian faith and others.
This would be unique to the Eastern & Oriental Orthodox, the Roman Catholic and the Anglican groups. The leader of the nation/empire/kingdom can call a "unity council" with another Christian faith. This unity council could have the potential to worsen or improve relations between faiths and between your own faith and yourself.
This could also be used to call a council to settle heresy. So for example, an Eastern Orthodox Emperor could call for a Church Council to deal with a heresy that has popped up like Bogomilism. The Church Council will involve both sides, and its result could be calculated based on the current demographics of the nation. If it has a "good" outcome, the amount of heretics will drop significantly. If it has a "bad" outcome, the number of heretics will increase and there is a chance that even you as the Emperor are asked to accept the heresy or be excommunicated (though this excommunication will not hold for those who don't hold the heresy), and if you are excommunicated, this could spawn an event which sparks revolution by heretical provinces.
These types of councils could be two-fold, one would be a "local council" which would only have affect in a region, or an "ecumenical (or universal) council" which would have an affect across the whole faith. The "ecumenical council" would activate events in other nations of your faith who can choose to send their Bishops, Clergy & Laypeople to the council to represent themselves. The local council would only be within your nation.
If your nation falls into heresy, then that could cause you to be excommunicated by the Pope (if your Catholic) or cause you to be excommunicated by other Orthodox Churches (if you're Orthodox).
Also, like previously mentioned, another council could be a "unity council" and this kind of council would be between your Christian faith and others Christian faiths, such as Eastern with Oriental Orthodox, Roman Catholic with Anglicans, Eastern Orthodox with Roman Catholics etc...
This decision will send events to all faiths involved. So if an Orthodox Emperor calls a unity council with Roman Catholics, it would send an event to the Pope and events to all Orthodox Churches who can choose to approve and send their representatives. This council will be one of the longest in game and once finished could have several endings. The worst ending would be disaster where relations with the other group is worsened severely. The neutral ending would be inconclusive with no loss or gain in relations. The medium ending would have relations improved between faiths, and the best ending would result in unity.
There could also be mini-events which wouldn't involve real theological examples, but would be little events that ask you whether you want to encourage your delegates to support your own faith or the other. The former could hurt your relations with the other faith, but improve those with your own. The latter could hurt relations with your own faith and improve with the other. However, the latter could also encourage the approval of the unity.
With this event, if it approves unity, then the groups will be united together as one faith. But if you pressured your delegates to accept it despite their opposition, then it could cause them to revolt and even excommunicate you.
If you don't pressure your side, you can avoid revolution and excommunication but it is less likely to result in a unity (depending on overall relations between the faiths). So it is up to you.
Another thing that could happen, is that if you're a Roman Catholic leader with a Catholic and Orthodox council, and the unity council is a success, then Roman Catholics (encouraged by the Pope) will accept it, but Eastern Orthodox will revolt against their leaders and oppose it.
Or if you are an Eastern Orthodox leader and unity is approved with the Roman Catholics, then Roman Catholics may accept and follow the Pope, but some small groups may create an "Anti-Pope" elsewhere in Western Europe.
What would be the advantages? The biggest advantage would be better relations, and if unity is achieved with the Roman Catholic Church, then the other groups can request crusades from the Pope. However, the Eastern & Oriental Orthodox would still be unable to participate in the Crusades.
Also, which faith you are could determine what the outcome is. If you're an Eastern Orthodox leader, and unity is achieved with the Roman Catholics, then the Pope will become the "first among equals" but will only have "control" over Western Europe. Or as Orthodox, if you achieve unity with the Anglicans, then the Archbishop of Canterbury will become the Patriarch of England.
Whereas if you are playing a Roman Catholic nation, and unity is achieve, with say, the Anglicans, then the Anglicans will become Roman Catholics under the leadership of the Pope.
(this can also depend on what decisions you make during the council, if you support the other side, then the end result will be their result)
This gives a good alternative to military conquest for altering the religious landscape of the map.
Conversion
There should also be an option/ability to convert to another religion. Converting to a completely different religion may destroy your powerbase (but could potentially save your nation from invasion by that faith). Converting to a different sub-group of your faith would be less severe and could also be strategic or based on preference.
Culture
I would like to see culture & race divided or have sub-groups. So if you take the medieval Russians, they will have a main culture and race of Russian, but a sub-culture of Byzantine, which will allow better relations with those with Byzantine culture.
Or with the Sicilians, they would have a primarily Italian/Sicilian culture, with a subculture of Byzantine.
Maybe you could also have multiple sub-cultures. A sub-culture could be based on a historical fact (such as the Byzantines converting & influencing the Rus) or based on national makeup (like Mongolians within Russia after Golden Horde dissolves).
