It should be a one class upgrade that's sold or offered by Avios miles on BA. However, from time to time, BA does opup one class to elites from all OW programs so they may "sample" the higher priced product (in hopes they'll buy it next time)...and not just if WT or WT+ is overbooked. I don't count on it, but it's happened to me twice this year (out of four long haul BA WT segments). Never got CW to F though when flying on a biz fare.

OP mentioned he's an AB/OWSapphire, but does he have AA miles with which to upgrade the AA flight(s)?