Let n ̸= 0 be an integer. We call a set of m distinct positive integers D(n)-m-tuple if the product of any of its two elements increased by n is a perfect square. The question of interest is how large these sets can be, i.e. how we can extend given triple with more elements. In this talk we continue our research of considering the extension of d(4)-triples of the form {1, b, c} for various parametric sequences of c. We prove that in such cases we again get the result which supports the well known conjecture, that every D(4)-triple can be extended to a quadruple with a larger element in a unique way. In the proof we use the standard methods, like solving the system of simultaneous Pell-like equations, congruence method, linear forms in logarithms and Baker-Davenport reduction.