Hi Tracy, sorry I just saw your post. Did you find an answer to your question? The CIPD employment law page on TUPE discusses fragmentation - scroll down to the section service provision changes involving two (or more) contractors:
www.cipd.org/.../

Hello, 

The concept of ‘fragmentation’ in the context of TUPE (Transfer of Undertakings (Protection of Employment) Regulations) typically arises when a service previously provided by a single contractor is divided among multiple new contractors. This can complicate the application of TUPE, especially in determining which employees transfer to which new service provider. CoveredCalifornia

In recent case law, there has been a shift towards allowing the contracts of employees to be split between multiple transferees. This means an employee could potentially go from working full-time for one employer to part-time for two or more employers post-transfer.

If the service is broken up to such an extent that it no longer retains its identity, TUPE may not apply due to ‘fragmentation’. It’s important to get legal advice tailored to the specific circumstances of the contract and the proposed changes to understand how TUPE might apply in your situation.

I hope it's helpful for you.

Best Regard,
Ryan