Good question.
I would advise you against playing "hard to get" in the traditional sense but definitely encourage you to use interviews as an opportunity to interview the prospective employer.
You can do this in a number of ways. One way is when they ask you a question ask for clarification or turn the question back on the asker. This could get you more information and also allow you time to formulate a stronger answer if one doesn’t come to mind immediately. Another way is to ask very thorough and engaging questions at the end of the interview.
Definitely appear interested in the job but you would also likely want to play it a little cool so you do seem like you have a number of opportunities that you are considering.
You could also maybe tighten up your answers to their questions. One thing you might not be doing in your interviews is speaking in specific terms. A lot of candidates will speak about their skills and contributions in general terms, especially if they worked in a highly collaborative environment. Practice framing your answers in the "problem, action, results" (PAR) style. When asked a question put forth a real world example where there was a business problem, articulate the action you took to address this problem, and share the specific result.
At the end of the day you want to leave prospective employers with a concrete vision of who you are and what you would bring to their position/company and the impression that you are interested.
If you play too hard to get you will risk being thought of as arrogant and might not get the job.
Hope this helps and good luck in your next interview.