MFC Boat Box - Large Fly Foam
This is the baddest mambo jambo there is. It's monstrous size can deplete the stock of a fly shop and ensure you have every fly you need out on the water. This is definitely a fly box aimed at boating enthusiasts or those that want a "mothership" at home they can pull flies from for their day trip our. 
This box can have separate leaves inserted into it that can accompany even MORE flies. 
The box is waterproof and has a sealed gasket system around the rim. This is great if you fish in saltwater or rainy conditions. Waterproof boxes ensure no water gets in - (and no water gets out). So, if you do happen to leave it open when a downpour occurs be sure to dry it out once your home!   
I (Ethan) have one of these for myself and love it. It holds an astronomical amount of flies. Not sure the specific number (those always seem to be overzealous anyways). 
What's beautiful about this box is: you can have it all in one place. No need to have a separate dry fly box, nymph, box, and streamer briefcase. You can fit them all in this and have plenty of room to spare! You can add the middle leaf to your preferences. Fish smallmouth flies mainly? Then get the large or XL slot. Need a billion hoppers for your trips out west? Get the small leaf size! 
13 x 4 x 10 inches