build-essential is the set of packages that are implicitly installed for building Debian packages. Intel compilers are sideways to this; I'm afraid this needs to be handled by way of the intel compilers (or packages thereof) being updated to recognize the /usr/include/<triplet> include path by default - because /usr/include/asm is *not* going to be the only bit moved around in /usr/include as a result of multiarch, just the most immediate and prominent one.
build-essential is the set of packages that are implicitly installed for building Debian packages. Intel compilers are sideways to this; I'm afraid this needs to be handled by way of the intel compilers (or packages thereof) being updated to recognize the /usr/include/ <triplet> include path by default - because /usr/include/asm is *not* going to be the only bit moved around in /usr/include as a result of multiarch, just the most immediate and prominent one.