Upvote:4
Russia has such a tight policy about where you can get visas from.
You can easily apply for a multi-entry visa, with sufficient proofs that you would like to visit there more than one time. Multi-entry visas are usually valid for 3 months or more, so it should be OK for your case.
Embassies of other countries do not usually care about what other usable visas you have. I have multi-entry visas for Malaysia in my passport, a double-entry Indian visa, both still valid, and I'm going to Nepal tomorrow. I'm almost sure I won't face any issues.