The authors investigate some questions related to \(\mathbb{A}^1\)-contractibility of Koras-Russell type varieties over an algebraically closed field \(F\) of characteristic \(0\). An algebraic variety over \(F\) is said to be \(\mathbb{A}^1\)-contractible if the structure morphism to \(F\) is an \(\mathbb{A}^1\)-weak equivalence ([F. Morel and V. Voevodsky, Publ. Math., Inst. Hautes Étud. Sci. 90, 45–143 (1999; Zbl 0983.14007)]). In [A. Dubouloz and J. Fasel, Algebr. Geom. 5, No. 1, 1–14 (2018; Zbl 1408.14078)] it was shown that Koras-Russell 3-folds of the first kind, namely the varieties in \(\mathbb{A}^4\) defined by \[ \mathcal{X}(n,\alpha_i,a)=\{x^nz=y^{\alpha_1}+t^{\alpha_2}+ax\} \] are \(\mathbb{A}^1\)-contractible. The main results of this paper are generalizations of this result: Theorem 1.3 states that the \(S^1\)-suspension of a Koras-Russell fiber bundle, as in Definition 1.1, is \(\mathbb{A}^1\)-contractible; Theorem 1.5 states that the \(S^1\)-suspension of an iterated Koras-Russell 3-folds of the first kind, namely a variety in \(\mathbb{A}^4\) defined by \[ \mathcal{Y}(m,n_i,\alpha_i,p)=\{x^{n_1}z=(x^{n_2}y+z^m)^{\alpha_1}+t^{\alpha_2}+xp(x,x^{n_2}y+z^m,t)\} \] is \(\mathbb{A}^1\)-contractible. The proof of Theorem 1.3 uses modifications to reduce the number of singular fibers and induction; the proof of Theorem 1.5 refines techniques in [loc. cit.] and [M. Hoyois et al., Algebr. Geom. 3, No. 4, 407–423 (2016; Zbl 1369.14031)] and a criterion for stable \(\mathbb{A}^1\)-contractibility.