How can steel manufacturer chemical composition differ from ASTM/ASME chem comp? 2

For Mn it does. See the notes in Sec. IIA SA-516 Table 1.

There is a product analysis tol for nearly all elements in metal alloys.
The Heat Analysis has to meet the specification ranges, but the product analysis has an additional allowance.
There is also the fact that they may be making a grade for someone with higher Mn that is not ASME (perhaps SAE or proprietary).

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P.E. Metallurgy, consulting work welcomed

In the past, added Mn above the 1.30% was permitted provided a reduction of C is provided within specific limits as I recall.

Yes Stan, there are grades where the footnote for C and Mn relates to a hardenability calculation.
This lets you run lower C and higher Mn than the base amounts.
The do this so that the steel can be used in a wider range of applications.

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P.E. Metallurgy, consulting work welcomed

Thank you all for the clarification, great responses.