"Stagger" really means to hold them at different times: not to hold them simultaneously. Here, however, the context indicates that the point is to hold them at times that ensure that they "feed into the Regional Programme Mid-Term Evaluation": in other words, that they are held before that evaluation. So really it is being used here just to mean "schedule".

I think the writer has probably used "stagger" with the idea in mind that they should be moved forward in time, if necessary, so as not to coincide with the Mid-Term Evaluation.

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Note added at 1 hr (2014-03-26 11:20:50 GMT)
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As I say, "stagger" is not really being used in its proper sense here, as far as I can see. Literally, "stagger the ongoing Country Office Iran/Pakistan and Afghanistan Mid-Term Evaluations" means not holding these two evaluations at the same time as each other. But since the object is simply that their results will feed into the Regional Evaluation, it wouldn't actually matter if they were held at the same time as each other, and in any case they are ongoing (i.e. continuous), so they are really bound to coincide with each other. But more importantly, it is no use at all holding the country evaluations at different times if one or both take place after the regional evaluation. The crucial point is that the country evaluations should be "staggered" in relation to the regional evaluation, and specifically that they are completed before, not after, that regional evaluation. Therefore the strict sense of "stagger", hold at different times (from each other), is not the intended meaning here; what the writer means is "schedule" or "programme" or "time".