Thanks for your question.
I assume that when you state " multiple visa" you are referring to a Multiple Entry Visitor's visa permitting him entry to the UK on multiple occasions throughout the course of the visa.
This being the case while it is physically possible for you to marry at a Registry office in the UK whilst here on that visa I would not generally advise you to do so. This is because the visa is for visitor purposes only. There is a special visitor's visa called a Marriage Visitor's Visa for visitor's who wish to come to the UK in order to marry:-
See Visitor's for the purpose of marriage at the bottom of the above link
If it is intended that he shall remain in the UK after marriage to settle permanently with you then he could have to apply for settlement before he came, which is different.
If it is intended that he marries here then returns to Russia for a period of time before returning to the UK to settle permanently with you later then at that later time he would have to apply for settlement.
If you require guidance on the eligibility criteria and basic supporting documentation/waiting times then please submit a further question to the bard again requesting me via my profile and I shall assist.
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