Can I use 兼 for more than two positions?
No, grammatically speaking, you cannot use any conjunction between more than two elements.

CEO兼CTO兼CFO  (✘)
CEO、CTO兼CFO  (✔)
CEO和CTO和CFO  (✘)
CEO、CTO和CFO  (✔)

I believe it's the same in English, instead of saying Alice and Bob and Charlie, you would say Alice, Bob and Charlie, right?

Another suggestion: you can use the word 兼任. E.g.

我是个创始者，但是由于我的公司因没钱而不能雇佣，现在我兼任CEO、CTO和CFO。