Rental Applications -- is it OK to have many for one home?

[RANJAY SINGH]

How many rental applications I can take in one time say while the property is vacant? Can I have new people submit new applications while the old one is still being processed? Is there a law that prohibits I cannot have more than one applicant at the same time for one home? Is it Ethical to have many people apply (while one is still in process)? as the application fee is non-refundable and 100% goes to the third party. They very well know they are not the only ones and clearly say application does not mean automatic approval. But I may lose good tenants and a LOT of time, If I do not do parallel processing or if I ask others to wait and not apply while the first one has applied but not supplied all information or says will submit document but just things are delayed. 

Any guidance? Also, whom will you choose, a person with 6K income 3 dependents or 3K income with no dependents? Please share your wisdom! 

Thanks in Advance to all responders!