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I've got a few demon prince compositions.
1: EXTRA TRYHARD- Tzeentch Prince with wings, power armour,black mace. I could also throw a sigil of corruption for a 3++ (MoT) and 3+. Like this, your prince can only be wounded on 2's, rerolls on 1 if it does go through and the reroll would result in a wound on 1 or 2. More or less it is an unkillable beast with a cursed AP2 mace.
2: TROLL PRINCE - A prince of your choice, wings and with a burning brand of skalathrax. Slap that HQ with one or two heldrakes and turn the skies into a field of fire. Watch your weebo space marines flee and cower in the sight of your low AP flamers.
3: Nurgle Prince with iron arm (daemons would work better than CSM on this) and slap options as deemed suitable. Iron arm D3 extra strength can turn the prince into S10 T10. almost unkillable machine. I would recommend power armour/warp forged armour and wings on this. Another unkillable engine in your almost cheesed to the fullest army.

This isn't how it works. DoT princes don't get +1 to invulnerable saves, they reroll rolls of a 1.

Mark of Tzeentch in the CSM codex offers a +1 to invulnerable saves to any unit that has it. ie: thousand sons has AODG plus MoT. They have 5++ plus +1 which makes their invul ++4 cos of mark of tzeentch. Search it up.