I don't know the technical limitations.
But since Intel intend to replace Beignet I would expect to have only one of them installed at a time to avoid potential conflict.
We encourage all the former users of Beignet and Classic to switch to Neo.
The result is a new and improved OpenCL Driver stack (informally known as “Neo”), that is intended to replace both previous closed-source driver (aka “Classic”) as well as the Beignet driver.
Beignet vs. NEO
Starting in Q1’2018, Beignet has been deprecated in favor of NEO OpenCL driver (https://01.org/compute-runtime).
We encourage the existing Beignet community members to explore the new driver stack and provide feedback.
Beignet remains our recommended solution for legacy HW platforms (e.g. Ivybridge, Sandybridge, Haswell).
Then again since Beignet has it's own icd file. Could that allow them to co-exist after all? I guess it would be revealed shortly after trying.
It installs the OCL icd vendor files to /etc/OpenCL/vendors, if the system support ICD.
I'm afraid that's all I can do now in an attempt to help
As this task has been marked Needs Maintainer for a month with nobody having stepped up to become maintainer, in addition to providing an acceptable patch for inclusion, marking as WONTFIX. Feel free to re-open when a patch has been submitted via the proper processes.