For the Fighter the Dueling and Two Weapon Fighting styles have have a Riposte feat allowing a strike to be made against a foe that critically fails an attack roll. In addition to this there exists 'Improved Twin Riposte' which grants an additional reaction to make a Twin Riposte and which can be used even if the Fighter is not benefiting from Twin Party, the first of the three-feat chain it comes from.
Could a Sword & Board Fighter take all three feats in this chain to enable Riposting with Shield in hand? They would meet the criteria of wielding a weapon in each hand so long as they use a Shield Spike and while Twin Party would be a little bit wasted as a feat for the Fighter who will be relying on raise a shield instead of the parry action the wording of Improve Twin Riposte would seem to allow this.
Am I overlooking something in my reading or should this work?