Can a DPE do a checkride in any plane of the same class?
FAA Order 8900.2B (General Aviation Designee Handbook) sets out the policy on Designated Pilot Examiners (DPE).
Verbiage from Chapter 7, Section 1 states:


Additional Qualifications. DPE applicants must be technically qualified and must hold all pertinent category, class, and type ratings for each aircraft for which designation is sought. All DPEs must meet the requirements of Title 14 of the Code of Federal Regulations (14 CFR) part 61, §§ 61.56 and 61.57, as appropriate.


And from para. 1. f (2) (a) of that section:

(2)    Meet all eligibility and experience requirements for the specific designation sought.
(a)    A designee applicant must have logged at least 5 hours as PIC in each make and model of multiengine airplane and helicopter in which that designee conducts tests.


In specific response to your question (using the guidance shown above in FAA Order 8900.2), it appears that as long as the DPE has been given the FAA authority/Designation to conduct the type of check you are requesting (i.e., Instrument Rating) he/she should be able to do it.
However, some DPE's are only authorized (by the FAA) to conduct Private Pilot examinations, others have additional authority such as Private Pilot/Commercial Pilot/Instrument, etc.
You should pose your question to the DPE directly for confirmation.