My experience, from having obtained 3 different multiple entry Russian business visas in the past 4 years, is that the application must be presented in your country of residence.
The whole process is a massive PITA, if you can find a visa agency to do the work for you, you won't begrudge them their fee.
Also be aware that it takes quite a long time (from 4 to 6 weeks) to get everything done.
Read the instructions provided on the forms very carefully. For example, if it says to fill in the form in black pen, be darn sure to fill it in with a black pen - I had one rejected because I used a (more common) dark blue ballpoint. Similarly, pay attention to the exact measurements specified for the photos.
Also be aware that you probably don't have to surrender your passport except at the very end of the process, and then only for a day or two. The initial application form only asks for a photocopy of the passport.
Michael
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