Several considerations follow from the requirement to make the AEO operation OK so far as OEI is concerned -
Providing that the AEO takeoff is constrained to
(a) remain above the calculated OEI profile at all times and in all circumstances
(b) remain at a higher energy state than the OEI profile
(c) track as per the OEI escape (this can be a problem with turn radius)
you will be able to sort out the failure case along the departure without too much angst.
There is the sideline consideration where the OEI tracking is different to the AEO departure. In this case, the ops eng group SHOULD have done the sums to make sure you stay sweet. I have it on good authority that such does not always happen .. about the only things you can do there is
(a) work for a good operator, as I have been fortunate to do
(b) make sure you have a good general knowledge of the subject so you are well placed to know when to ask awkward questions ...
The devil is in the detail and it is NOT amenable to winging it on the fly.
Your ops engineering folks are paid to do the sums for you and, indeed, the company's normal operating procedures should be incorporated into the OEI special procedures so the pilot ends up with a one size fits all for each runway procedure ....