You can use multiple は grammatically, although consecutive use of it sounds weird a little. But basically in Japanese sentence we have only one subject, as well as in English sentence.
Because "は" is not "to be" verb, but an adverbial (or binding) particles which strengthens the meaning of the preceding word, the word followed by は is not necessarily a subject, and whether it becomes a subject or not depends on the word and the context.
今、私は忙しい - strengthens I
今は、私(が)忙しい - strengthens Now
今は、私は忙しい - strengthens both I and Now
The last example leads one word to cancel out the importance of another word. That's why multiple consecutive use of は sounds weird.
And in all 3 examples, 私 is always a subject and 今 is not. Theoretically 今 can be a subject, but I don't come up with a good example right now.