Each bank and credit card issuer has different rules around how long you need to wait between applications. But, our strategy recommends waiting 90 days between applications with the same bank or issuer.
This means, we are not going to recommend you open 2 Chase cards within the same 90 day period. Although, there are no real drawbacks when mixing providers. For example, you are fine applying for a Chase, Citi, and American Express credit card all in the same day.