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The intersection dimension of a graph $G$ with respect to a class $𝒜$ of graphs is the minimum $k$ such that $G$ is the intersection of some $k$ graphs on the vertex set $V\left(G\right)$ belonging to $𝒜$. In this paper we follow [ Kratochv’ıl J., Tuza Z.: , Graphs and Combinatorics 10 (1994), 159–168 ] and show that for some pairs of graph classes $𝒜$, $ℬ$ the intersection dimension of graphs from $ℬ$ with respect to $𝒜$ is unbounded.