Thank you Jennifer for your question to "Ask Extension".  I am requesting that you send me additional photos of the underside of the leaf and the tree as a whole.  Are the leaves with the spots at the top of the tree or at the bottom of the tree or generally all over the entire tree?  How is the tree receiving water if at all besides normal rainfall?  When did you first notice the spots on the leaves?  Is the number of leaves with spots increasing?  Approximately how old is the plum tree?  Have you recently fertilized?  The photos and answers to these questions will be helpful in the further diagnosis.
     I look forward to hearing back from you.

Mostly at the top, though there are some lower. 

     Thanks for the quick response.  In general your plum tree has leaf spot.  The two basic types of leaf spot are fungal and bacterial.  In the Willamette Valley you would lean towards fungal infections because of our long damp months.  But the yellow halos around the spots were difficult to match with other photos of fungal leaf spot.  So I pursued bacterial infections and found that Xanthomonas ssp. infections had yellow halos that turned to yellow leaf and leaf drop.  But . . . Xanthomonas infections are found east of the Cascades and usually in curcurbit vegetables.  So you should first work on mitigating a fungal infection.       Cultural control for fungal infections include:  
Prune trees for good air circulation
Rake and destroy leaves in home garden 
Chemical control for fungal infections include:
captan, chlorothalonil, myclobutanil, or propiconazole.  Organic fungicides contain copper.  When using chemical controls always follow the label instruction
     I would take a wait and see approach to see if cultural controls  are helpful in reducing or eliminating the problem and how much it is going to affect the trees vigor in the future.  You should also look for fruit infection and/or reduction of fruit yields.  
     OSU does have a plant pathology clinic that can identify the specific organism but they charge a fee.  The current fee is $87.  I have provided you with a link to the clinic below.

https://bpp.oregonstate.edu/how-submit-plant-materials

If you have additional concerns or question please feel free  to respond.