Dear Cindy
first some question to you:
which EHSM/EHS module you would like to use? (for explanation see: Environment, Health and Safety (EHS) - SAP Library)
My list would be:
a.) EHS-BD
b.) EHS-SAF
c.) EHS-DGP
d.) EHS-SAF-GLM (may be)
e.) EHS-HSM (may be)
f.) EHS-WA (less probability)
g.) EHS-HEA (less probability)
h.) EHS-IHS (may be) (or do you would like to use "Component Extension for SAP EHS Management?)
Regarding your scenario:
So all 3 companies would contiue to maintain their own SAP system and their master data required for EHSM will be sent via ALE so they will continue to have one system of record.
Depending on the answers to the question above you might go in "wrong" direction. Especially if you need EHS-DGP and EHS-SAF-SVT or EHS-SAF-RSH this is a "bad" option. You should ask for help SAP or a SAP partner definiing a suitable SAP Landscape.
I have the feeling that you do not understand all aspects of EHS. E.g. the topic of "vendor", "Customer", "Material" data is very critical for EHS and anything here must be "unique".
Let us assume now this example:
You have four SAP Systems
SAP System 1 does use client 100; SAP system 2 does have as well client 100; same for SAP System 3. Now If I understand you correct you would like to establis SAP system 4 as well with one client (let us use first simple example); once again this might be done in client 100.
Now you would like to establish ALE distribution from SAP System 1, 2, 3 to SAP System 4 regarding master data (e.g. materials etc.). SAP system 4 would be used as a "master data reference system" for EHS/EHSM management. The main issue with this approach is: you need EHS data as well in SAP system 1,2,3 especially if you need to use or would like to use EHS-DBP; that means you need to establish backward ALE starting SAP system 4 to 1,2,3 in regards of DG management; And now comes the "bad" news: to do the backward ALE you need to establish basic EHS customizing in SAP system 1, 2, 3.
First conslusion: in this sceerio you will execute at least basic EHS customizing in four SAP systems (may be you feel now like: 
)
Conclusion: your SAP landscape is a "nightmare" (and not only for EHS/EHSM set up):. Therefore: ask SAP or a SAP partner to help you to consolidate your SAP landscape or to think about suitable options in regards of EHS/EHSM set up; on long term you will not get happy with this situation.
C.B.
PS: please refer to this general SAP Note as referenced in this link for classic EHS installation: EH&S installation: Composite SAP Note
This is a must to read note. If you need on the top "Component Extenstion for SAP EHS MAnagement:
PLease check: SAP EHS Management for Beginners
You will find a lot of references to other threads regarding the "Challenge" in the use of "Component Extension for SAP EHS Management)
PPS: good luck for you and your team; this is a quite challenging IT project