It depends on the grade of oil.
GII base oils have better (lower) volatility than GI, and better cold pumpability properties. GII+ are better than GII in these respects too. And GIII are better yet again .
To blend a SM 5W oil (5W-20, 5w30), GI can't meet the NOACK of 15% and the cold spec's at the same time. GII isn't even good enough by itself to make the 15% spec., so it needs to be upblended with (50-60%) Group II+. You could possibly blend a little GI in a SM 5w30 (maybe 15% or so), but if you do, the motor oil will require even more GII+ or GIII correction fluid to make the spec.s, making the oil more expensive. So there is a cost incentive to use only GII or above in the 5W-20 and 5w30 SM formulations. If you buy a 5W-20 or 5w30 SM motor oil, you are pretty well guaranteed of getting only GII and above oils.
10W-30 SM oils are a different matter. SM 10W-30's should be able to be blended with majority GI and some GII/III correction fluid, but I would think more correction fluid is needed for SM compared to the previous SL spec. because of the increased thermal/oxidative requirements. SM also brought in a sulfur limit which may exclude some GI base oils.
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What about 10W-30? For GF-4, can it still be made with Group I base oils? What are Correction Fluids?
Most Group I base oils cannot be used for GF-4 10W-30 without some help. Higher VI base oils, called correction fluids, can provide this help. Depending on the properties of the Group I oil used, the final blend might require 10-50% of a correction fluid, such as 5R. If a Group III correction fluid is used, less will be required.
Another problem with Group I oils is that they have higher concentrations of impurities, such as aromatic compounds, and sulfur and nitrogen compounds. These impurities accelerate oxidative degradation. So, in addition to needing help with viscometrics and volatility, Group I oils need help to meeting the requirements of oxidation tests, like the Sequence IIIG engine test. Therefore finished lubricants formulated with Group I base oils formulations require boosted additive packages to achieve similar performance to engine oils blended with Group II.
While it is possible to blend GF-4 10W-30 using mostly Group I base stock meeting spec will require more expensive correction fluids and more expensive additive packages.
Here in N.A. (Canada, US) because the base oil supply for passenger cars and vehicles is almost all GII, SM 10W-30's should be virtually all GII based because the supply availability for GI blending is going to be limited. Outside N.A. GII availability is limited compared to GI, so the chances of running into a GI majority based SM 10W-30 is a lot higher.
There were quite a few 10W-30 SL (previous spec. which has the same 15% NOACK as SM) blended with majority GI and some GII/III correction fluid even here in N.A. If I walked into some store and they had some motor oil on sale -- say,
Bob's Deluxe Motor Oil …
…SL rated -- 5w30 and 10W-30. Unless I knew the 10W-30 was GII based, I would only buy the 5w30. If unsure about a SL or SM rated 10W-30, the "trick" is to buy the 5w30. The 5w30 guarantees you a large majority GII+ based motor oil if not all GII+ since there is no way to use any significant amount of GI and meet the spec's.
The situation for the SM heavier grades like 10W-40, 15w40, 20W-50 would be similar. Here in N.A. they are almost all GII. Outside N.A. they are likely mostly GI based (with some correction fluid).