select m1.dealer_id
     , m1.manager as manager1
     , m2.manager as manager2
     , m3.manager as manager3
  from dealers as m1
left outer
  join dealers as m2
    on m1.dealer_id
     = m2.dealer_id 
   and m1.manager
     < m2.manager  
   and m2.manager
     = ( select min(manager)
           from dealers
          where dealer_id = m1.dealer_id 
            and manager > m1.manager )
left outer
  join dealers as m3
    on m1.dealer_id
     = m3.dealer_id   
   and m1.manager
     < m2.manager         
   and m2.manager
     < m3.manager                
 where m1.manager
     = ( select min(manager)
           from dealers
          where dealer_id = m1.dealer_id )

An ON clause associated with a JOIN operator is not valid.  SQLSTATE=42972