CJ, it depends on what the trauma's are though.... its not just a blanket statement about multiple trauma, as every single human being suffers multiple trauma within their life. What its about is the intensity of multiple trauma. If a person was raped, that usually comes with more than just being raped, ie. beaten, bashed, any after effects physically, then the mental aspects of being raped. One trauma has multiple aspects.
Any person with complex PTSD would typically not be a candidate near immediately. Quite bold if a therapist went near someone with complex PTSD. Severe PTSD, also not a good choice as the trauma is too intensive.
If a person has multiple trauma, depending on the trauma itself, works through that trauma and openly talks about it, then maybe EMDR could be an option to find or recover any hidden aspects and bring them out. From what I am aware, there is a criteria in which must be met first to be capable of under-going EMDR. What that is I do not know, but typically a therapist must first analyse all aspects of the trauma and use commonsense as to if the person is holding out from them or not. If they are, usually they will be rejected for EMDR. If the person is quite open and talks about the worst and most secretive issues, even keeping some to themselves still, they will usually fit the mold to have EMDR because they are more open which means less surprises and less chance of something going wrong.
The problem if it goes wrong is brain impairment. This means, in a small dosage you could experience reliving your trauma on a heightened daily response. Basically your trauma is going to worse in your mind. If the damage is medium, the brain nearly fries itself, you could find some pretty serious states of shock, convulsions daily, loss of motor skills, etc etc.
If it totally went wrong, your looking at being pretty much a vegetable. The therapist would have to be a moron though to push someone who wasn't responding already to the treatment though to that level. That would be negligent on the therapist behalf if anything ever got that bad.
The person giving EMDR unfortunately cannot control your mind, nor do they know what is going to popup from within it.
You have to have some trust in your therapist, though if you personally are in doubt of the treatment, its immediately not the right treatment for you. You must be allowed to make your own decisions on what is best for you.
EMDR is a very good treatment, and it is becoming a first line of defence for therapists nowadays due to its success at helping to heal trauma. It is not a cure for PTSD. It is a cure for anxiety only disorders. It is a very good treatment for trauma. It is not a cure though, never has been. EMDR has come a long way, will continue to evolve. The facts are though, it does pose certain risks and those must be disclosed to you. If the therapist is blase about their interview process whether your viable for EMDR or not, then you will ultimately suffer, not them.
I would not say to people to be scared of EMDR, or run from it, or wipe it totally from being a viable solution to help heal your trauma... far from it. What I would say is that if you have doubts over your therapist, if you have doubts and are keeping a lot of information secret from your therapist, and I mean heavy hard hitting trauma, then you may want to make the decision for yourself and not put yourself in such a high risk because your simply not ready to heal. Once you get talking and have no more secrets, then you would be more a candidate for EMDR to work effectively for you, not against you.