I only know it because I did look at the differences between instructor ratings JAA --> EASA in detail to decide what to do myself (I went for FI).
An FI can do this - it says
Originally Posted by EASA FC 905.FI
(b) class and type ratings for single-pilot, single-engine aircraft, except for single-pilot high performance complex aeroplanes ...
(b) single-pilot multi-engine class or type ratings, except for single-pilot high performance complex aeroplanes
I have no idea if it is intentional that there is no TRI for "single-pilot high-performance non-complex" nor for "single-pilot non-high-performance complex" aeroplanes.
It looks like that someone decided to limit the CRI, and forgot to make the CRE consistent or think about whether that should mean a TRI should be able to do this.
FoxRomeo, what are you actually after? If you are a CRI and have been instructing on a DO 228, I would write a letter to the CAA and ask them in what way your current privileges will be transferred once EASA comes into force - they came up with an answer for IMC rating holders (national licence with anational rating), perhaps there will be a pragmatic solution at least until 2014, which will work as long as you use it in the UK.