Water removal from an outdoor below grade stairwell

I have an 80 year old house with a basement walkout that floods in heavy rains. The drain that's there was disconnected before we purchased the house and cannot be reconnected without breaking up a good portion of my basement.

Is there anyway (pump or otherwise) that I can get the water ejected from this stairwell in a rain?

My other alternative is to cover the stair well up since we don't use it very often and have the water diverted before it even gets to the stairs.

dig a hole

you will probably have to dig a pit under that stairwell
and simply put in a sump pump and pump tha tout onto the yard...

water

The immediate solution would be to get the blue Little Giant sump pump that will pump to within an eighth of an inch from the concrete floor. Once that is done you can decide if you want to do anything further.