With regards to CPL training, the answers given so far are basically correct.
With regards to IR training (which I know is not what you asked about, but it's been included in the thread creep), first of all we need to clear up some terminology. An IRI is not a Flying Instructor. An IRI is a pilot who has not done the FIC, but who wishes to teach people for the IR.
Since you are already an FI, you will never be an IRI. What you will be if you want to teach for the IR or the IMC is an FI with the "No Applied Instrument" restriction removed.
To remove this restriction, if teaching the IR, you need to have 200 hours of flight under IFR. If teaching for the IMC rating, it's just 40 hours IFR. In both cases, if you've been logging time by sole reference to instruments (i.e. either actual IMC, or simulated IMC) rather than IFR (i.e. on airways, etc, following the rules of IFR, whether IMC or not), then divide these times by 4, so that's 50 hours by sole reference to instruments for the IR, or 10 for the IMC.
Although we're not really talking about the IRI, it's worth mentioning that the requirements for this are 800 hours IFR or 200 hours by sole reference to instruments.
With regards to both CPL and IR training, though, the other hurdle is to become a multi-engine instructor. Although it is possible to teach a single-engine CPL or a single-engine IR, and it is possible to teach the single-engine components of the multi-engine courses, you will make yourself far more employable if you are a multi-engine instructor.
The requirements for this are 30 hours of P1 on multi-engine piston aircraft (so your own CPL/IR does not count, except for successful skills tests, because it's not P1). 10 of these hours must be within the last 12 months, and ME SPIC time does not count. After that, it's a 5 hour course and a test. For me, this is the biggest problem, because the cost of building 30 hours P1 time is very high - I'm working towards it slowly, but still have quite a way to go.
FFF
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