If you split it down the middle you'd have 2 2x4's...then you could just glue them bck together
That's splitting hairs, so to speak. Technically, you could use a 2x8, but you would also have to use a 2x4 according to the initial rule. I don't want to say what you can and cannot use. If you can honestly say, "I used a 2x4 to make this." you've satisfied the one and only rule.
The spirit of the build is to limit yourself to use something undesirable, or just not worthy of a build. A 2x4 is not an ideal size so you will have to cut it somehow. It's probably not the greatest tone wood either, probably too soft, yadda yadda yadda. We know all that. But can you sew a silk purse from a sow's ear?
I feel all zen-like now.