Can hydride shift and methyl shift happen one after another in a carbocation?
Multiple rearrangements can happen if the resulting species is stabilized by it. In general hydride shift is more favourable over methyl shift because of its smaller size.    

The example proposed by James was not known to me but its truly an amazing example.   


  James:
  It’s possible for multiple hydride/alkyl shifts to occur. One amazing example is in the biosynthesis of lanosterol.  
  
  Multiple shifts are certainly possible, and they could happen, but generally will only happen if each shift generates a successively more stable carbocation.
  For example, you probably wouldn’t see a shift if it involved turning a tertiary carbocation into a secondary carbocation.


Source  

From Wikipedia: