VeeAny,
You have pulled up a rule which concerns 'crew members other than flight crew'; the appropriate rule is JAR-OPS 3.980 (to which there is an AMC and additional provisions in Appendix 1 to JAR-OPS 3.005(f) - for small helicopters).
JAR-OPS 3.980 Operation on more than one type or variant
(See AMC OPS 3.980)
(a) An operator shall ensure that a flight crew member does not operate more than one type or a variant unless:
(1) The flight crew member is competent to do so; and
(2) Appropriate procedures, approved by the Authority are included in the Operations Manual.
This is not a type rating issue (as others have said, there is no limitation on that) but one of limitation on operations for the purposes of Commercial Air Transport (CAT). The text provides adequate provision for alleviation but, as you would expect, there have been many discussions about the application of the policy - particularly when addressing larger helicopters.
The AMC provides
a method of compliance which permits two large types (over 5,700 kg) or three small types to be operated. It becomes more complex when mixing large and small types; in a recent interpretation of the AMC by one State (in which EASA was involved), a ruling was made that operation of any one large type restricted operations to two type (two large, or one large and one small).
This ruling might have been influenced by the types being considered: 5,700 kg is a break above the complex medium twins (S76, EC155, B412 etc.).
A more sympathetic policy might be applied to the smaller singles; JAR-OPS 3.005(f) had a provision categorising these into 'groups'; this was an early attempt at simplifying the rules.
Notwithstanding this, the rule was provided so that the carriage of passengers for hire would be conducted to a higher standard of competence.
jiggyman524,
One of the problems is the way you have posed the question. To my knowledge, there is no restriction on the number of types that can be on a licence or operated commercially; the rule which is described above applies only to CAT operations - other commercial flying is not affected.
Jim