The hardest basing options I've seen for the MX were the various super hard silos, I believe 3,500 atm hard silos were actually built, or otherwise considered "certainly achievable", and 7,000 atm were considered "possible"; the Deep Base, where MX missiles would be stationed about half a mile and change underground along with Air Force crewmen, base personnel, and a team of tunnel bore crews, after the bombs fell the crews would dig themselves out egress tubes over several months, eventually break the surface, and fire their missiles; and the Deep Silo/Hard Rock basing, of which LANL's "Pencil Pusher" could resist surface bursts up to 100 megatons, while Boeing's "Sand Silo" could resist 25 megatons, both presumably direct impacts.
https://books.google.com/books?id=Zz8rAAAAYAAJ
https://books.google.com/books?id=VD8rAAAAYAAJ
https://books.google.com/books?id=PJf2jZbIPjcC&pg=PA267&lpg=PA267&dq=super+hard+silo+50,000+psi&source=bl&ots=N2DI3yPUb3&sig=zQ5N2zx2C6zgCxWfWUT1XOE9XNQ&hl=en&sa=X&ved=0ahUKEwiXtdOdjbzRAhXJ7YMKHRpKDDwQ6AEIHjAB#v=onepage&q=super%20hard%20silo%2050%2C000%20psi&f=false
I'm not sure how good these Google book scans are, what's omitted I mean, but they contain enough info for what I talked about.