This work is concerned with maximal subgroups of \(S=\text{Sym}(\Omega)\) where \(\Omega\) is a set of infinite cardinality \(\kappa\). Known examples include stabilizers of finite sets, ``almost'' stabilizers of infinite sets \(\Sigma\) where \(| \Sigma|< \kappa\), and ``almost'' stabilizers of finite partitions. We produce new maximal subgroups containing stabilizers of subsets, filters and partitions, which are all in some sense almost stabilizers of these structures. We consider groups which contain the pointwise stabilizer of some set \(\Delta\subset \Omega\) with \(| \Delta^ c| =\kappa\). Any maximal subgroup containing such a group is either the almost stabilizer of a finite partition or is the stabilizer of a nontrivial filter. Furthermore, we have a complete analysis of all maximal subgroups containing the stabilizer of a filter with a linearly ordered filter base. We also define almost stabilizers for partitions with infinitely many parts of the same finite or infinite cardinality, and show that these groups are maximal. The problem of determining which filters have stabilizers which are maximal leads us to introduce closed and superclosed filters. If a maximal subgroup is the stabilizer of a nontrivial filter then the filter is unique, closed, and, unless the group is the almost stabilizer of a set, superclosed. However, there are closed and superclosed filters whose stabilizers are not maximal.