Lots of folks do this; some even experiment to find optimal location for each tube type.
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I have a CJ premier 14, CJ used GE's and Sylvania's when they could get syl...now they use GE's and unmarked tubes that are labeled Gt Britain, which I'm assuming are Mullards.
I've used all Mullards, 2 Mullards and 2 Hitachi's, and stock GE and Sylvania, all offer a slightly different sonic picture. So I think you can mix n match as long as the tube type matches.
Go crazy with it, there is no harm in experimenting with different brands. I've even tried mixing 6922's with 6DJ8's in my former CAT pre...no problems with good results.
I do recommend better tubes for the inputs and decent tubes for the outputs (gain) sections. If you have a phono section place your best (or quietest) tubes there.