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If you think of a multi-grade oil like a grade you would get in school, it might be based on 2 parts - attendance and participation. You have different requirements for attendance than you do for participation and you can't get a grade without both.
In multigrade engine oils, it's the same, you can't have a multigrade oil without 2 parts - the XW designation (for low temperature performance) and the 8, 12, 16, 20, 30, 40, 50 or 60 that follows(for high temperature performance). Just like the school grade you have different requirements for the low temp portion of the grade and for the high temp portion of the grade. For the low temp portion it is based on the ranges of low temperature cranking and pumping viscosity, and for the high temperature portion it is based on ranges of kinematic viscosity and a minimum HTHS.
If your grades in school went A, B, C, D, E you couldn't get an A unless you met the requirements of both the attendance and participation portions of the grade.
For grades in engine oil, you can't get a 5W30 unless you meet both the cold temperature requirements and the high temperature requirements for that grade.
Now sometimes you will find a straight grade engine oil (ie SAE 40) this is old nomenclature and is for those people who went to school when all they cared about was attendance. It's not really used anymore because engines are much more complex now and require us all to pay closer attention and start participating.
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Typically an oil company will have several base oil "cuts" with different viscosity grades. These are typically sold based on SUS viscosity (100N 220N etc) for Group I and II and based on cSt@100 for Group III and synthetics (4cSt and 8cSt being the most common) although this greatly varies depending on the supplier. Depending on the grade and whether it is a synthetic, synthetic blend or conventional fluid they will create a mixture and strategically use the viscosity modifiers (PPD's and VII's) to meet the target viscosity at the best price.
Also complicating the issue is what specification claims they want to make with their product. In order to make API claims for example the formula has to pass expensive engine sequence testing. To reduce cost the API allows a certain level of base oil interchange where tests do not have to be repeated for a new base oil as long as certain guidelines are adhered to. The same is true of OEM specs like Dexos1 although the base oil interchange rules are usually much more restrictive with OEM's.
Often the final blend of base oils and viscosity modifiers comes down to a combination of what the blender can buy most cost effectively and what their additive supplier partner (who is probably the one who ran the engine tests) can support with the program that was developed for their specific DI choice.
What you have read is incorrect because the tests which give you the 10W portion of the grade ARE NOT THE SAME as the ones that give you the SAE30 portion. See the above example comparing the SAE grade to a school grade which has 2 parts.
The oil blender will use a balance of base oils and VM's to meet the target viscosity window for the full grade (ie 10W30) not take one oil grade and then "magically" try and convert it to another grade. I have yet to see an oil formulation that doesn't use some VII - including full PAO formulas. I have seen some with very little (ie less than 3%) but never one that is completely VII free - despite what people on the internet will tell you about esters and pao formulations.