7 of 7 Added mention of multiple sources of Advantage

Negation of Advantage

At our table we use the Variant Flanking rules, however we noticed the same problem as yourself, and added the corollary that you cannot gain Advantage from a Flank if you yourself are being Flanked. The thematic justification was that you are busy trying to cover your own back and can't put all of your attention onto exploiting the enemy's defensive gaps.

This is justified mechanically under the rules for gaining advantage and disadvantage:

The GM can also decide that circumstances influence a roll in one direction or the other and grant Advantage or impose Disadvantage as a result.

It led to players holding formations, covering each others back and using the terrain more to their advantage, using low walls and pillars to block enemy movement into the now more limited flanking positions.

It may be worth noting that at our table, while we do not grant Advantage to a Flanked Flanker, we don't actually class them as having received disadvantage for purposes of "multiple cases of advantage and disadvantage do not stack". Effectively meaning that any other source of gaining Advantage would still be enough to give the player an edge. This was done as else spells such as Darkness and Guiding Bolt lost a fair amount of utility. YMMV on this however.