[RadioKid]

I'm sorry, multiple "HA" is not grammer issue.

>私はイタリア語は話し ます。

This is not wrong. And also most of native Japanese will accept it in a talk.
But in written form, it seems strange. Native Japanese will omit "私は" here because you alerady indicate the main theme in the first sentense.

multiple "HA" in a sentense is not an issue of grammer but they will make confusion because the listener can not find main topic when complicated expression follows after multiple "HA".

I always check my writing to avoid multiple "HA" in a sentense. In this case, I would write, (assuming you only speak Italian)

私は日本語を話しません。イタリア語だけです。

In your example, I wonder why you focused on Italian in your second sentense and will ask "How about English or other languages?".