What are the requirements for a PPL to upgrade from SEL to MEL?
The appropriate paragraph of Part 61 of CFR 14 is 61.63 (emphasis mine, the 'unless' part does not apply in your case):


  (c) Additional aircraft class rating. A person who applies for an
  additional class rating on a pilot certificate:
  
  (1) Must have a logbook or training record endorsement from an
  authorized instructor attesting that the person was found competent in
  the appropriate aeronautical knowledge areas and proficient in the
  appropriate areas of  operation.
  
  (2) Must pass the practical test.
  
  (3) Need not meet the specified training time requirements
  prescribed by  this part that apply to the pilot certificate for the
  aircraft class rating sought; unless, the person only holds a
  lighter-than-air category rating with a balloon class rating and is
  seeking an airship class rating, then that person must receive the
  specified training time requirements and  possess the appropriate
  aeronautical experience.
  
  (4) Need not take an additional knowledge test, provided the applicant
  holds an airplane, rotorcraft, powered-lift, weight-shift-control
  aircraft, powered parachute, or airship rating at that pilot
  certificate level.


So, to answer your question, no, you do not need a cross-country, you do not need any solo time in a multiengine airplane, either. All you need is a sign off from your instructor.