Can I use 兼 for more than two positions? 兼 takes two objects that are in the same category. For example,

一般来说，在IT行业一个中小企业创始者担任CEO兼CTO是常见的。
在我的家庭，妈妈是个厨师兼清洁工。

However, can I add one or more, and make it more than two positions, such as:

我是个创始者，但是由于我的公司因没钱而不能雇佣，现在我担任CEO兼CTO兼CFO。

Or is it only for 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。