I'm not sure, but the leaves having a mid-vein sounds like Star of Bethlehem, Ornithogalum umbellatum. The bulb on this would look like a little onion. You'll know better when it blooms. If it is Star of Bethlehem, it can be very weedy, just so you know. Maybe you can try googling an image..?

It does sound like it could be Star of B, although I don't remember them having a large number of leaves per bulb. If it has white starlike blooms, it is Star of Bethlehem. Cheleinri isn't kidding saying it is very weedy. In zone 6 these can make huge clumps in a short period of time, & I understand they can spread by seeds as well. I think zone 4 is pushing the edge of their range though, so you may not have as much trouble from them.

Mine do have a bunch of leaves per bulb. When I bought this house I was so excited at all the crocus that came up in the spring..talk about disappointing! :P I just got finished pulling them from the back bed this weekend. I don't know what to do about all the ones in the lawn.