Bud,
Your solution for drainage at the lower level (basement) and the stair will suffice for surface flow building up only in those locations. The issue is with the grading as it passes by the stairs down to the basement. The surface sheet flow from the grading will easily overwhelm the drains on the stairs and at the lower landing (which also tend to clog up with dirt and debris throughout the year anyway). My suggestion is to divert surface sheet flow along the grading with either an extended wall, a curving wall or even a bio swale, such that water cascading down the slope will not have unfetter access to the basement stair. Water rarely flows uphill when properly diverted. Your French drains and drain tile system will do the rest.

Thanks,
Ricardo Ramos, Assoc. AIA, LEED® AP, CSI

I understand the intent, but this solution will result in a flooded basement even under the slightest rain fall. A more appropriate solution would have turned the access into the basement toward the patio adjacent fire place. The plinth of the patio would have provided sufficient grade change to avoid flooding into the basement area as well a better connectivity between those two outside spaces.

This is a common problem we have encountered with daylit basement solutions on shallow sloping sites. The site drainage issues are critical with such designs.