Splicing house circuits together?

I'm planning on getting a very powerful welder.
I'm don't really think our puny 15 A circuit breakers can handle the massive amount of current it will draw though.
I've heard of welders being plugged into circuits meant for stoves, but my stove's circuit isn't easily accessible from where I want to weld.
I was wondering if it is possible (and safe) to splice together circuits in parallel. As in, is it safe to take the supply of one 15 A circuit, and splice it together phase to phase with a different 15 A circuit? (You know, like, without burning anything down. Specifically, my house.)
When you connect two circuits in parallel, the amperage adds, so it should get me a good 30 amps, right?