Listed below are a list of mods that I've checked for compatibility with East Empire Expansion and found no conflict. If any of these are incorrect please let me know ASAP. Patches by other authors can also be found on the forum post.
I'll update this list as I test EEE with more mods:

Alternate Raven Rock by Jerv1
Azuroas Raven Rock by Jaipebbles
Azorod's Whiterun by Azorod
Better Courier by Korodic
Brokenbluff by Lordamuel
Civil War Refugees by Ceftadzime
Cliff Cabin by Lametrie
Dawn of Skyrim Director's Cut by Vaelka
Epic Cities Solitude by FaramH
Epic Windhelm Expansion by leontristain
Fortified Whiterun by Skyfall515
Greater Markarth Expansion by Domenicus7
JK's Windhelm Outskirts by Jkrojmal
Kingdom of Eastmarch by Axis1211
Kingdom of Falkreath by Axis1211
Kingdom of the Rift by Axis1211
Mandragora's Winterhold Overhaul by Mandragorasprouts
Markarth - City of Stone by Amasido
Menskr (Vanilla and COTN versions) by DexModsOfficial
Northern Raven Rock by Caenraes
Lawbringer by EpicCrab
Legacy of the Dragonborn by Icecreamassassin et al. (don't put relics into any LOTD containers)
Provincial Courier Service by Arthmoor
Prettier Decorated Roads by Retrophyx
Raven Rock Reimagined by Overseer666
Riften Docks Overhaul by marxercise, flintone, zebra0, Urtho, AgentW, and robertgk2017
Rockin' Raven Rock by GreyMtnFox
Ruined Winterhold by SillySilverSongbook
RYFTEN by Yuril
Solitude Expansion by Ceasirius
Tel Aschan by Elianora
The Port City of Windhelm by pancake0723
White River Farm by XxLeafeater27xX
Whiterun Expansion Redone SSE by Gamerdude092 (original) and marob307 (SE port)
Windyridge by Mandragorasprouts
Winterhold Trader by MlemandPurrs (SE) and ImmBasic (original)