  We construct complete Calabi-Yau metrics on non-compact manifolds that are
smoothings of an initial complete intersection $V_0$ that is a Calabi-Yau cone,
extending the work of Sz\'ekelyhidi (2019). The constructed Calabi-Yau manifold
has tangent cone at infinity given by $\mathbb{C} \times V_0$. This
construction produces Calabi-Yau metrics with fibers having varying complex
structures and possibly isolated singularities.
