Can you go into multi system organ failure with no obvious cause?

No: There will be a reason for it. However it may not be possible to diagnose the exact underlying cause for it as it is the complication and sometimes unfortunately the end point of many diseases (however usually basic assessment and tests will give clues). Sometimes if a patient passes away with this an autopsy would be needed to establish the cause

Multiorgan failure: No. Just need to look harder for cause.