Summary: The \(b\)-Exact Multicover problem takes a universe \(U\) of \(n\) elements, a family \(\mathcal{F}\) of \(m\) subsets of \(U\), a function \(\mathsf{dem}: U \rightarrow \{1,\dots,b\}\) and a positive integer \(k\), and decides whether there exists a subfamily(set cover) \( \mathcal{F}^{\prime}\) of size at most \(k\) such that each element \(u \in U\) is covered by exactly \(\mathsf{dem}(u)\) sets of \(\mathcal{F}^{\prime} \). The \(b\)-Exact Coverage problem also takes the same input and decides whether there is a subfamily \(\mathcal{F}^{\prime } \subseteq \mathcal{F}\) such that there are at least \(k\) elements that satisfy the following property: \(u \in U\) is covered by exactly \(\mathsf{dem}(u)\) sets of \(\mathcal{F}^{\prime } \). Both these problems are known to be NP-complete. In the parameterized setting, when parameterized by \(k\), \(b\)-Exact Multicover is W[1]-hard even when \(b = 1\). While \(b\)-Exact Coverage is FPT under the same parameter, it is known to not admit a polynomial kernel under standard complexity-theoretic assumptions, even when \(b = 1\). In this paper, we investigate these two problems under the assumption that every set satisfies a given geometric property \(\pi \). Specifically, we consider the universe to be a set of \(n\) points in a real space \(\mathbb{R}^d\), \(d\) being a positive integer. When \(d = 2\) we consider the problem when \(\pi\) requires all sets to be unit squares or lines. When \(d > 2\), we consider the problem where \(\pi\) requires all sets to be hyperplanes in \(\mathbb{R}^d \). These special versions of the problems are also known to be NP-complete. When parameterized by \(k\), the \(b\)-Exact Coverage problem has a polynomial size kernel for all the above geometric versions. The \(b\)-Exact Multicover problem turns out to be W[1]-hard for squares even when \(b = 1\), but FPT for lines and hyperplanes. Further, we also consider the \(b\)-Exact Max. Multicover problem, which takes the same input and decides whether there is a set cover \(\mathcal{F}^{\prime}\) such that every element \(u \in U\) is covered by at least \(\mathsf{dem}(u)\) sets and at least \(k\) elements satisfy the following property: \(u \in U\) is covered by exactly \(\mathsf{dem}(u)\) sets of \(\mathcal{F}^{\prime} \). To the best of our knowledge, this problem has not been studied before, and we show that it is NP-complete (even for the case of lines). In fact, the problem turns out to be W[1]-hard in the general setting, when parameterized by \(k\). However, when we restrict the sets to lines and hyperplanes, we obtain FPT algorithms.