Postgres multiple joins

just do another join on that same table:

SELECT animal.ID, breed1.BreedName as BreedName1, breed2.BreadName as BreadName2 
FROM animal 
   LEFT JOIN breed as breed1 ON animal.breedID=breed1.ID 
   LEFT JOIN breed as breed2 ON animal.breedID=breed2.ID 
WHERE animal.ID='7';