Fix multipart parsing when additional newlines are present

[pgjones]

Replaces #2762 and fixes #2761.

Checklist:

• Add tests that demonstrate the correct behavior of the change. Tests should fail without the change.
• Add or update relevant docs, in the docs folder and in code.
• Add an entry in CHANGES.rst summarizing the change and linking to the issue.
• Add .. versionchanged:: entries in any relevant code docs.
• Run pre-commit hooks and fix any issues.
• Run pytest and tox, no tests failed.

[pgjones]

Test failure is unrelated.