"I am a sleeping man."
Translation:저는 자는 남자입니다.
This sentence is technically correct, but wouldn't it be wonderful if the course developers had chosen sentences that are actually used and useful in both languages. If 1000 Koreans and Americns were canvassed, I doubt you would find even 10 who had ever uttered either phrase.
The sleeping man worked all night. The man sleeping is sick. The sleeping person is a man. There are so many possibilities. --or change the verb. I am a working man. I am a joking man. I am a welcoming man. I am a drinking man.
The second 는 is not a topic particle. It is the Korean method of changing a verb into an adjective, of changing an action verb into a descriptive word. In answer to your question, it is indeed possible, maybe even common, to have more than one 는 as a particle in the same sentence.
If you want to keep the meaning of "to be", (also known as the copula or connecting verb), the noun is always attached directly to it..
Or you could do this using different words:
나는 잠자는 사람입니다.
... "I am a sleeping person." Still we have noun + 입니다.
The woman is sleeping.
The woman sleeps. 여자가 잔다.