I am of the mindset that joining in to anything just to be closer with another person seems like time that could be used to do something alone together. I have yet to hear any of my friends that haven't been negatively impacted by playing that card.
My cousin requested I become friends with a new boy in the village. The outcome for her is he just wasn't interested, but I had a new best friend. It's just wrong to create situations in hope you become closer.
The oddest moment was being invited to his 50th Birthday because the last time that I had seen him was his 16th. We went outside to chat. He laughed when I admitted we were only friends because of the ultimate scheme. 'I will not believe that. You became part of the family and stopped my brothers from killing each other and did my paper route when I was away' A hug and a promise to do better keeping in contact fingers crossed.

My confusion is, "how does one get closer to someone by, going through someone else?"

Fuuuuk no! It will Not bring anyone closer in the way you want

Hell to the NO!

I'd never get into a menage a trois with the opposite sex. With the same sex yes, but not to get close to anyone.