When the Caralan's Ceremonial Plaza ("CP") was introduced, it played a new and unique role in the early game: A second "anchor" in each territory that you could build off of. Normally you have to wait until the medieval era (III) to build hamlets as a second anchor in a territory.

A few months later, harbours became anchor points.  This is cool, but it steals most of what made the CP a special emblematic quarter.  Sure, the CP gets a little amount of faith per adjacent district, but that was never its primary benefit.  So, with its unique benefit of coastal "anchor" being shared with the harbour now, should the Ceremonial Plaza get another buff?

To play off of the Caralans' other core benefit — adjacency bonuses — the first thing that comes to mind is to make it a better anchor than the harbour can be.

• At its simplest, maybe have the Ceremonial Plaza gain the additional properties of "counts as a Farmers Quarter, Makers Quarter, Market Quarter, and Research Quarter (and Commons Quarter?)" so that quarters placed next to the EQ become even better versions of themselves.
• Alternately, the CP could instead get a bonus like "+2/+3 Food per adjacent Farmer's Quarter, +2/+3 Industry Per Adjacent Makers Quarter, etc." similar to how the Babylonian, Egyptian, Harappan, Nubian, and sort of Olmec EQs all get heightened bonuses from adjacencies.

Either of these changes, or a change like it, would make the CP more compelling again as an alternative to the recently-buffed Harbours, while also playing into their core strength of adjacency bonuses.

What do you think about removing the Stability penalty, making it count as a Commons Quarter and giving it "+3 Food per adjacent District" in addition to the Faith? 

"In these public places, ritual food offerings are made to the gods. [...]

During these frequent ceremonies, inhabitants of the surrounding areas would come together to commune. A large variety of foods were then shared and consumed before being burnt as offerings. The many bone flutes found at these sites suggests that music also played an important part in these events." [reference]

I had another idea: what about making it count as a CQ, removing the ability to exploit all yields, removing the stability penalty, and doubling the adjacency bonuses of all surrounding districts?
In this way two FQ adjacent to both each other and the CP would obtain +4 Food (this would improve even further their LT)

PS: Maybe it should just be able to be placed also next to fresh water (ex: river, lakes, oasis)

Just came across this thread... very interesting ideas!

I can see how the making it a "counts-as-all" quarter would fit well with the Caralan legacy trait. It would also be interesting trying to save an adjacent spot for the Swiss to put down a Watchmakers Guild later on. It would also work really well with the district-boosting luxuries (Saffron, Silk, Gemstones, Silver) and would probably encourage forming early trade connections with those. IMO, it would still be good without the "counts as market" effect or a stability boost.

For my two cents, I was thinking of something even "simpler" that would be unique (at least to the Ancient Era) and also fit in flavor-wise: simply make it a Religious District.

It certainly fits with the district's description; in fact I was a bit surprised it wasn't one already!

No other culture in the Ancient Era currently has a RD

The versatility of the RD bonuses as your religion advances fits thematically with the versatility of the legacy trait.

The "anchor" effect would be more to help establish a firm lead in the religion race by triggering the faith bonus.

There are enough RD-boosting Emblematic Quarters in later eras (Sacred Mound, College, Ashram) that it could make for a fun, if not terribly powerful, RD-focused run-through.

Compared to the previous suggestions, it would be a much more modest "power" boost and more a pivot to a niche role. Possibly avoiding some power creep and expanding less explored/exploited aspects of the game.