There is one issue that is typically not addressed in the quickie ME courses and that is fuel planning. In SE flying we are taught that fuel left on the ground is useless and that we should carry as much as we can, only leaving some behind if we have to meet gross weight limitations.
Multi engine changes this, because having more fuel than you need, limits your options, and ability to climb out, when you lose an engine. This is especially true in low power twins, many of which have very poor, or negative, ability to climb on a single engine at gross; however if you are 10-20% under gross they do ok.
Performance is a matter of Weight:Excess Horsepower, so you want your weight as low as you can go so 50% HP is greater than required to maintain the required climb gradient at take off.
There is also the matter of briefing every take off so you know where your best options between chopping both throttles or continuing on OEI change.