I had three assignments due in at the same time on the same day during my MSc, it's a pain but it's doable if you plan your time well. For reference I had a 3500 word risk assessment, a 2000 word law essay and a 3500 consultancy essay to do, plus a 3500 word literature review due two weeks before.
I started the most difficult one first and left the easiest one till last. It was difficult I'm ngl but at least two of them were fairly straightforward.