There's several games in the series that have mods with campaigns that can be ran. Ones that I know of are:
• Mental Omega - Already added to the series with a few mission runs. Really well made and well polished, but the difficulty is absolutely ridiculous. Tread lightly. • Twisted Insurrection - Also already added but with no runs yet. Stand-alone mod that doesn't require Tiberian Sun. Also well made. • The Dawn of the Tiberium Age - Combines the best parts of Tiberian Dawn and Red Alert 1, including the factions. Not much of a campaign yet. Also stand-alone. • Rise of the Reds - Mod for Zero Hour. Adds Soviets and Europe as factions and overhauls the existing ones. Plans on having a campaign. • Renegade X - Re-creation of Renegade brought to Unreal Engine 3. Have not been able to install this so I'm not 100% sure their campaign is complete. • OpenRA - Open source re-creation of Red Alert 1 with competition in mind. Also has mods for Tiberian Dawn and Dune 2000.
This isn't all encompassing, just the ones I've noticed a lot. I'll be happy to add one once someone does a run of it.
Do you know if Cold War Crisis (A mod for Zero Hour) has a campaign too?
If it does, might be something to consider.
CWC does have a campaign. DTA has a Soviet vs Nod campaign with 8 missions. There are two other campaigns and several lone wolf missions as well. There is a Code Lyoko themed mod of YR that features a RPGish campaign, much like the Yuriko campaign from Uprising. (http://en.codelyoko.fr/jeuxvideo/)