Can I run NM 12 ga circuits on a running board or MultiCable Staples across floor joists use in a basement with an unfinished ceiling?
According to NEC 334.15(C) you can run NM cable on running boards exposed in a basement.
304.4(D) refers to running parallel to framing members but the stackable cable clamps could be consider support in this case. There is nothing in the code that I know of regarding the number of cables under one staple. You would have to refer to the manufacturer's instructions on the staples and their capacity.
The &quot;bundling&quot; you are referring to I believe is here:

310.15(B)(3) (3) Adjustment Factors. (a) More Than Three Current-Carrying Conductors. Where the number of current-carrying conductors in a raceway or cable exceeds three, or where single conductors or multiconductor cables are installed without maintaining spacing for a continuous length longer than 600 mm (24 in.) and are not installed in raceways, the allowable ampacity of each conductor shall be reduced as shown in Table 310.15(B)(3)(a).

The question here is the intepretation of the word &quot;spacing&quot;. I would argue having them on the same board next to each other or in one of those stackable clamps is properly spaced. The clamps are sold and apparently approved for just that propose.
And here:

334.80 Ampacity Where more than two NM cables containing two or more current-carrying conductors are installed, without maintaining spacing between the cables, through the same opening in wood framing that is to be sealed with thermal insulation, caulk, or sealing foam, the allowable ampacity of each conductor shall be adjusted in accordance with Table 310.15(B)(3)(a) and the provisions of 310.15(A)(2), Exception, shall not apply.
Where more than two NM cables containing two or more current-carrying conductors are installed in contact with thermal insulation without maintaining spacing between cables, the allowable ampacity of each conductor shall be adjusted in accordance with Table 310.15(B)(3)(a).

Notice this is only when run through an opening to be caulked or insulated or in contact with thermal insulation. Most jurisdictions don't consider it bundling to run multiple cables through bored holes or on a running board together. However, others want only two cables or less through the same hole. Check with your inspector to be safe.
Good luck!