Given a version number MAJOR.MINOR.PATCH, increment the:
MAJOR version when you make incompatible API changes,
MINOR version when you add functionality in a backwards-compatible manner, and
PATCH version when you make backwards-compatible bug fixes.
Additional labels for pre-release and build metadata are available as extensions to the MAJOR.MINOR.PATCH format.
What you're describing is build metadata.
Build metadata MAY be denoted by appending a plus sign and a series of dot separated identifiers immediately following the patch or pre-release version. Identifiers MUST comprise only ASCII alphanumerics and hyphen [0-9A-Za-z-]. Identifiers MUST NOT be empty. Build metadata SHOULD be ignored when determining version precedence. Thus two versions that differ only in the build metadata, have the same precedence. Examples: 1.0.0-alpha+001, 1.0.0+20130313144700, 1.0.0-beta+exp.sha.5114f85.
Following MAJOR.MINOR.PATCH-prerelease+BUILDMETADATA and since you didn't mention any prerelease status:
If instead he switched to 2.0.0 I would expect it to be a breaking change that meant I would have to rewrite my stuff to make it work because of incompatible API changes. If that isn't true you're losing customers for no good reason.