Is a CFII required in order for a flight Instructor to provide training for added class ratings?
An instructor need not be a CFII to provide training for an additional class rating to an existing instrument pilot with a category rating under which the additional class falls.
If a customer already holds a commercial airplane certificate with a single engine class rating and instrument airplane rating, an instructor does not need to hold a CFII to provide training that customer’s multi-engine class training.  My regulation walk is laid out below.  Please read it before voting or commenting.
Important note: if the customer is NOT instrument rated and is seeking the instrument rating for the category -and/or- the customer is seeking to upgrade from a PPL to a CPL or CPL to ATP, the instructor must hold a CFII/MEI.
Regulation Walk
First, when is an instructor required to hold a CFII?
61.195(c) outlines instructor limitation and qualification related to the instrument training.  This reg specifies that an instructor must be a CFII to provide instrument training for the issuance of an instrument rating, a type rating not limited to VFR, the commercial certificate, and the ATP certificate.
If we stop there it sounds like an instructor needs to be a CFII to provide training to a customer seeking a simple ME class add-on to an existing airplane SE comm-inst.  But wait…
Are we really conducting “instrument training” while preparing for an additional class rating to an existing SE comm-inst ticket?  No, we’re not.  “Instrument training” has a definition in 61.1:

Instrument training means that time in which instrument training is
received from an authorized instructor under actual or simulated
instrument conditions.

61.1 also defines “flight training” which is different from “instrument training&quot;:

Flight training means that training, other than ground training,
received from an authorized instructor in flight in an aircraft.

The training for an additional class rating to an existing airplane SE comm-inst is not “instrument training,” it is flight solely by reference to instruments and that’s an important distinction.  It sounds pedantic, but the FAA intentionally uses these two terms very carefully:
61.109(b)(3) – PPL airplane multi-engine aeronautical experience requirement

3 hours of flight training in a multiengine airplane on the control
and maneuvering of an airplane solely by reference to instruments,
including straight and level flight, constant airspeed climbs and
descents, turns to a heading, recovery from unusual flight attitudes,
radio communications, and the use of navigation systems/facilities and
radar services appropriate to instrument flight.

61.129(b)(3)(i) – CPL airplane multi-engine aeronautical experience requirement

Ten hours of instrument training using a view-limiting device
including attitude instrument flying, partial panel skills, recovery
from unusual flight attitudes, and intercepting and tracking
navigational systems. Five hours of the 10 hours required on
instrument training must be in a multiengine airplane.

Do you see the difference?  It’s carefully written to allow a non-CFII to conduct PPL ME training but requires a CFII to perform CPL ME training (which is also true for CPL SE).  But wait, there’s more…
61.109 and 61.129 are aeronautical experience requirements for the PPL and CPL certificates.  Note that our customer already holds a CPL certificate for airplane SE and an instrument airplane rating.  The instructor does not need to meet the hour requirements in 61.129 because 61.63(c)(3) [Additional Class Ratings] gives us:

A person who applies for an additional class rating on a pilot certificate…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.

This means that no “instrument training” is required and that any training that takes place is “flight training solely by reference to instruments” and can be performed by a MEI without a CFII.
So, to conclude…
…a customer seeking to add a ME class rating who already holds a commercial pilot certificate for single engine land airplane with and instrument airplane rating is not receiving commercial certificate training because he/she already holds a commercial certificate.  They're merely adding another class to their commercial certificate.
…a customer seeking a ME class rating who already holds a commercial pilot certificate for single engine land airplane with and instrument rating is not receiving instrument training because he/she already holds an instrument airplane rating.  Again, just a class add-on, not a new rating.  There are no ME or SE instrument ratings, it's a category rating.
…the training received is purely multi-engine operation training and covers how to exercise the privileges of their existing commercial pilot certificate and instrument airplane rating while flying a multi-engine airplane.  It is not training for an instrument airplane rating (they already have it) and it’s not commercial certificate training (because they already have it).  It’s an additional class rating per 61.63.
…our CFI/MEI (no CFII) can give the training and endorse the customer for a practical exam.
Important notes:
A customer seeking to upgrade a cert from PPL to CPL -or- CPL to ATP must receive training from a CFII/MEI.
A customer going for an initial instrument rating must receive training from a CFII/MEI.