Bob.
What a complex subject!. I'll deal with the mounted infantry element. The 1st, 2nd & 6th (Militia) battalions of the Manchester Regiment each raised a MI Company in its own right.
Additionally, following the outbreak of war in 1899 a Mounted Infantry Regiment was raised consisting of battalions each composed of four infantry companies from different regiments, although the King’s Royal Rifle Corps later provided a complete battalion. Their role included guarding convoys and lines of communication, working as advance and rear guards, reconnaissance and protection of field artillery batteries. Eventually at least twenty-seven MI Battalions of this Regiment were formed in addition to the individual Light Horse and Mounted Rifle Battalions which were raised locally or overseas from the empire.
The complete 1st Manchester MI Company eventually served as a company in the 27th MI Regiment.
Individual soldiers of the Manchesters did serve with many of the other MI battalions - as and when required.
Unfortunately not very much has been recorded about this subject. Perhaps something you could research in detail!!.