I was wondering if I would be able to do this without my head exploding. I learn a lot of progressive metal and I'm assuming anyone else who does would be able to understand why I would hit walls quite frequently with this style of music. When I hit said wall I'll go off and do some dreadful exercise for a while or practice improvisation for a bit and then go back to the song. This gets boring pretty fast and kind of sucks the fun out of my learning process. So I wanna know if I could actually take on like 2 or 3 songs so that if I hit a wall with one I can just jump to another one for a little bit and then go to another one and just kind of repeat this process. Would this be a good idea? Or would it be too much for my mind to try and remember how to play 2-3 different songs in such a short amount of time?
Depends on your brain and memorizing. For example I can easily learn few different songs at once. Learning one song at time is just plain boring for me.
I progressed mostly by learning multiple songs in the same period. I play mostly thrash metal, and there are many similar rhythm patterns, but slightly different. So when I hit a plateux with one song, I put it on rest and start learning different one, and by the time I learn that, when I come back to the previous one, it's easier to play beacause it consisted of similar elements with the one I learned but on a little different way and I had positive tranfher. That's fun way of learning. At least for me.
Depends on your how good of a musician you are, and what you are learning.

When starting out i only learned one song at a time, but now that i have been playing for so long i often have three songs at the same time in my practice, all in different styles. I think the thing to consider is that if the tunes are too difficult, then you might be doing yourself a service only practicing one at a time, but if you can handle the difficulty of the tunes, then you are free to expand.
Fusion and jazz musician, a fan of most music.

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I always like working on several songs at once. I feel it improves your overall technique, as opposed to just working on one specific example of that technique as it pertains to a certain song.

And it's a lot less boring too.
Usually I do 2 or 3 depending on what songs they are.

If I am learning some old school rock or metal IE AC/DC, Metallica, Van Halen, Black Sabbath etc etc. I can learn a few at a time.

If I am learning something like technical like Dream Theater, Animals As Leaders, Scale the Summit, Steve Vai etc etc. Then maybe 1 of those songs mixed with an easier song(s).

All depends. I also like to have 1 day a week where I just warm up and get loose. And play through all the songs that I am learning/enjoy to play. Like a mini concert practice. That way I can hyper focus on try to ace them with a one time go-around. This way I can find parts of songs that I need to work on for the next practice session!

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Thrashturbating? Most metal of all ways to pleasure oneself.