We are not totally without information on plume penetration. A very special NASA DC-8 documented ash levels, sizes, and gas concentrations and the details are all there for those who have the time to read it.
Here
I quote from the report on the inadvertent ash incident with the NASA DC-8, a fully instrumented airborne science research test bed.
More than 100 commercial aircraft have unexpectedly encountered volcanic ash in flight and at
airports in the past 20 years. Eight of these encounters caused varying degrees of in-flight loss of jet
engine power (ref. 1)
and
Reference 5 explains
that a range of damage may occur to aircraft that fly through an eruption cloud depending on the
concentration of volcanic ash and gas aerosols in the cloud, the length of time the aircraft actually spends
in the cloud, and the actions taken by the pilots to exit the cloud
The airplane was re-engined with four CFM56-2 engines prior to delivery
to NASA.