This is very complicated matter and greatly varies from country to county I have noticed.
There are authorities who allow and grand TRI training based on approved TRTO and EU-OPS requirements, even though actual type would not be approved on said TRTO's approval.
Then again, there are countries who do not accept anything except actual proved TRTO TRI training authorization for specific type.
It took me few years to get my first one, and when I expanded it to second type, the local authority demanded amended hours to syllabus set by MAJOR European airline's TRTO.
It is a rocky road in some places, but still in my opinion worth of it, IF someone is paying for it.
Good luck!