Answers

Many of the EIFS issues we see are related to improper flashing, etc.  These types of issues can be repaired by removing EIFS in affect area installing PROPER flashing as patching EIFS.  Done by a professional craftsman the repair can be seamless.

You can also remove all of the EIFS and install any kind of material to the house.

+1 to Jeffrey's answer below. 

Most of the observed deficiences that we see in EIFS are the result of poor installation and flashing details.  Almost all the push off failures that are seen now are the result of poor water management and water getting behind the EIFS and pushing it off the substrate. 

See if it can't be fixed and flashed properly before ripping it all off.