forget about dominance ... thats not your problem.. the problem is .. and work with me here .. lol ... you have a weak crotch with included bark .... swear to GOD .. here.. i'll prove it to you .. lol ...

https://duckduckgo.com/?q=weak+crotch+with+included+bark&t=ffcm&iax=images&ia=images

who would have thunk it.. eh ??? ... lol ...

flip back to the web side and read up a bit...

i would probably remove everything on the right.. in the last pic ...

all that said.. if emerald ash borer are an issue in CA.. just get rid of it ... consult your county extension office ... presuming you are totally certain on the ash ID ....

ken

ps: all trees releader ... and loss of dominance is NEVER a terminal illness ...

The few Autumn Purple ash I've seen around here, including my own, look like yours. I assume it's the nature of the beast. So far as included bark and multiple crotches, that too is common to the eastern ash species. My tree has endured multiple ice and wind storms and has come through like a champ, but I'm not especially fond of its growth pattern, or fall foliage, or...

Agree with latter observation.

The big Fraxinus family Ash here really don't grow in a christmas tree shape when planted in the open. I have three in various degrees of sun which are am excellent example.

My plan would be:

-check on EAB and see if it lives in your climate. If it does your tree has a limited life expectancy or will need treated regularly to maybe survive.

-prune to keep too many branches from forming at the exact same spot. My big Fraxinus americanas seemed to like to do that and 50 years down the road 3 of the 4 had multi-crotches (check that word out ken!) which honeysuckle would sprout in and water would seem into.

This is a long term thing though which cost the ones over my house their lives in their 60's. You can prevent it now with minimal effort and are correct to be thinking about it.

Fraxinus is actually a genus, of course. California Cooperative Extension should have information about the pest question. They have web pages as well as branch offices.

The classic pruning handbook The Pruning of Trees, Shrubs & Conifers by George E Brown says once ashes form rival leaders leading to a rounded head, as they are often inclined to do then long and heavy main branches that are prone to breakage later are in fact apt to result. (It also says, ironically in this instance, that American ash tends to retain its leader well). So now that yours has already made a big bush maybe you will want to replace it with something else. Apart from the possible borer issue.

Also this species makes a quite large tree in time, well over 60 ft. tall - and perhaps therefore too big for your situation.

Embo, the clone Autumn Purple that I've seen as mature trees have a branching habit like the tree in the OP, as mine, which is about twenty years old, does. It grows nothing like typical white ash. I personally don't care for the shape of the tree, and here in TN at least, fall color is an unattractive muddy purplish-brown. I would not recommend it in the mid south, EAB aside

Embothrium, I am to lax in my verbiage on classifications. Partially because I disagree with how many species there are, partially sloppiness on my part.

Hello from Scottie Ash Seed, your specimen was originally discovered in the wild somewhere in NW Illinois or SW Wisconsin by Carl Junginger back in 1950's. American White Ash iconic for excurrent form similar to sycamore. While both Elm, Ash and Sugar Maple one of only few proven to handle lower trunk diverging multiple stems similar looking to a maturing pipe organ. White Ash wellproven to mature between ages 350-450, and some lived past age 600!

But never fear, as an Arborist structurally pruning hundreds of young trees under age 20, myself and others have proven no matter codominant stems advancement. By subordinating or heading back each competing trunk, turning it into a slower growing lateral. Trunk attachments ratio will slow girth enough to halt both bark and zylem inclusion. This way slower growth rate kept in check will allow for more normal branch collar set up to return while main trunk gets larger. Then once co-dominant leader kept small for few yrs can be removed so fat lip tissue closes over.

If you do not worry about temporary misshapen crown, restoring apical dominance will pay off huge, taking within less than five years. This season I would immediately subordinate all vigorous growing branches pointing upward to slow down growth rate on either one or other diverging trunk. Retaining curving one could be cool option. Or continue with keeping straighter one, but only head back its lower temporaries then turned into slower growing laterals that give new skinnier upper main trunk added girth and needed shade.

Give me few days and I will diagram possible removals using your photo. And don't let anyone scare you about Emerald Ash Borers arrival. Its well worth conserving way cool purple fall tree, here is link to my historical EAB blog where I teach owners how to self inoculate trees with natural Neem. And bunch of photos of Chicago's oldest ash trees I conserved! https://scottieashseed.wordpress.com/