EER Diagram - subclasses which are neither disjoint nor fully overlapping
Assumptions:


A service can be of either type A or B. Not both.
A request can be for either a service of type A or for two services (one of type A and one of type B).
A client can have many requests.


I think a clean option is to have a Service_Request entity which associates the entity named, say, Client and Service. It will have 2 attributes, service_a and service_b where the second is optional. In SQL:

CREATE TABLE service_request
( service_request_id INT NOT NULL
    PRIMARY KEY,
  client_id INT NOT NULL                    -- who ordered it
    REFERENCES client (client_id),
  request_ordered_at TIMESTAMP NOT NULL,    -- when it was ordered
  -- more details about the request
  -- (price, duration, etc.)

  service_a_id INT NOT NULL                 -- type A service
    REFERENCES service_a (service_id),      --   (mandatory)
  service_b_id INT NULL                     -- type B service
    REFERENCES service_b (service_id)       --   (optional)
) ;


The rest of the design, the entity Service and the two subtypes (Service_A and Service_B) should stay as they are in the question.