Sounds like you want to make another SHA256 network/coin which would make it yet another altcoin. Only BTC is Bitcoin and there is only 1 Bitcoin network. ALL others, even those using SHA256 - are altcoins. Period.
Yes, technically I want to make an altcoin. But I just want it to... watch it happens! Mining, sending, receiving. That's all. I own 2 computers and this idea came up to my head.