Suppose Bill is a bachelor and Marcus is married. I claim that <Bill is a bachelor> stands in the same relation to <Bill is a never-married marriageable man> as <Marcus is a bachelor> stands to <Marcus is a never-married marriageable man>. But the propositions about Bill are true while those about Marcus are false. Since grounding is a relation that holds only between truths, the relevant relation that the two pairs of propositions have in common is not the grounding relation. It is something else. Call it ontological explanation, following Dan Johnson's dissertation. (Since, I think, explanation is factive, so that only truths can be explained, and they can only be explained by truths, ontological explanation isn't explanation strictly speaking.)
Abbreviate "<x is a bachelor>" as bx and "<x is a never-married marriageable man>" as nx. Then, necessarily, for every human being (at least) x, nx ontologically explains bx. Let B be Bill and M be Marcus. Then, nB ontologically explains and grounds bB, while nM ontologically explains but does not ground bM.
Moreover, we are in a position to offer a grounding for the proposition <nB grounds bB>. This grounding is given by the contingent truth nB and the necessary truth <nB ontologically explains bB>. So at least in this case, the grounding truth is itself grounded in a truth about Bill together with a necessary truth of ontological explanation.
So at least sometimes we can find a grounding for grounding truths partly in terms of ontological explanation truths. This gives some evidence that ontological explanation facts are more primitive than grounding facts.
Is this pattern in general true? Is it the case that if p grounds q, then p together with <p ontologically explains q> grounds <p grounds q>? Not if ontological explanation is like Johnson thinks it is. For Johnson thinks that that if a ontologically explains b, then a is metaphysically necessary and sufficient for b. But p can ground q without being necessary for q: that I am sitting grounds that I am sitting or standing.
Perhaps we can modify Johnson's account by holding on to the sufficiency while dropping the necessity. Then we will have something like ontological explanation where a ontologically explains b only if a is metaphysically sufficient for b. In that case, the general pattern might hold. What grounds that <<I am sitting> grounds <I am sitting or standing>>? It is <I am sitting> and <<I am sitting> ontologically explains <I am sitting or standing>>. Of course, the falsehood <I am standing> also ontologically explains that I am sitting or standing.
If this is right, then we can get below the hood on grounding: the more primitive notion is ontological explanation (modified from Johnson's account as above). If Johnson is right to require necessity, we still can get below the hood on grounding in some cases.
Here is one reason all this might matter. Consider propositional desires other than beliefs. Let's say Marcus wishes he were a bachelor. It is important, both to Marcus and to the analysis of the situation, that <Marcus is a bachelor> is ontologically explained by <Marcus is a never-married marriageable man>. There is something about being never-married, or being marriageable, or being a man, or a combination of these that implicitly appeals to Marcus. (Likewise, ontological explanation seems potentially relevant to Double Effect.)
One could try to handle the stuff about ontological explanation by using counterfactual grounding. The relation between nx and bx is that nx would ground (or would necessarily ground) bx were nx true. But it is implausible that such a counterfactual fact is prior to the grounding fact if x is Bill.