Biquard–Minerbe [8, Theorem 2.4] use singular perturbation methods to solve a complex Monge–Ampère equation on the minimal resolution of $(\mathbb{R}^{3}\times\mathbb{S}^{1})/\mathbb{Z}_{2}$. Using the more general approach adopted in this paper to glue hyperkähler structures one could extend their construction to recover a $6$–dimensional family of $D_{2}$ ALF metrics.