Damn, and I though I was long-winded

All that just to say -the affects of a Field Hospital's Medical Service ability unit and the HQ Support unit's Medical Service ability are cumulative... which they are not.
The 10% speed increase of the Pioneer element (Pontooneer unit and various other flavor units)
may be cumulative with the 35% speed increase of the Engineer element (Engineer unit and various other flavor units), because they are different abilities. The Medical Service ability of the HQ Support unit and the Field Hospital unit are however the same ability, and I know of no abilities that are cumulative of the number or elements which enjoy those abilities.
Testing for cohesion loss is not a one-shot-cut-n-dry process; there a chance variable in cohesion loss for units. Additionally the terrain being moved through, even the loyalty and MC of the regions, affect cohesion.
If you want a more cogent demonstration of how abilities are not cumulative, take the following 4 types of units and put them into the same region: 1. a flavor unit consisting of a single elite infantry element, eg: Bull Run Bde, 2. a flavor unit with a number of elite elements, eg: Irish Legion, which has 5 elite elements, 3. any infantry brigade, 4. a leader with which you have created a division with the infantry brigade in 3.
Check the Maximum Cohesion of an infantry element of the normal unit in the division and write it down. To do this, break down the division, select the normal unit in the Stack Panel so that its constituent elements are displayed in the Inspection Panel, select an infantry element of the normal unit -write its name down- and click on that element's NATO symbol in the Inspection Panel. In the element detail window, in the lower-left box it will show the element's cohesion values -"Cohesion: xx/yy"- where "xx" is it's current cohesion and "yy" is its Maximum Cohesion. Write down the Maximum Cohesion value.
Now recombine the normal unit into the division and add the Bull Run Bde, or what ever single element elite unit you have selected, and run the turn without doing anything else with the division.
Elite elements have the Strong Morale ability

"This element is either composed of highly motivated, battle-hardened individuals or is a leader capable of inspiring his men. The inspiration provided gives a +5 Maximum Cohesion bonus to all other elements of the unit."
Since a division is a unit, if there is a single elite element in the division --the Bull Run Bde-- each element of the entire division will have its Maximum Cohesion raised by 5.
You have to run the turn to see this change, because what you are doing on the map is actually only planning. It does not occur until the turn runs. In fact, if you turn the "Focus on Move" option off and center your display on the region, once the game is through plotting the enemy faction's move and other things, right after is says "Loading Master File" you can see that the Bull Run Bde is
not in the division; it's there to see in the region. As soon as the first day starts it will be put into the division; you can see the Bull Run Bde disappear from the map and the strength of the division increase.
Now check the Maximum Cohesion value of the same element of your normal brigade as I described above. You will see that the Max Coh has risen 5 points.
Now add the Irish Legion into the division too and run a turn. If the Strong Morale ability were cumulative the element of the normal brigade will not have its Max Coh raised by 5 points, but by 30(!!) [6 * 5].
One thing that is calculated for the player immediately is cohesion recovery. Take any unit with lowered cohesion standing in a town region, but outside the town, and check its tool-tip for its cohesion recovery per day; "Average Cohesion: xx/yy (Variation: z.zz / day)". Now drop that unit into the town and check it again. You will find that the recovery rate will have risen substantially.
Take a Field Hospital and an HQ Support unit and do the same while stacking the unit with one, the other and then both at the same time. You will find that regardless of which you stack it with --or both-- that the rate of recovery is the same.