How to use BehaviorRelay as an alternate to Variable in RxSwift?

Have you considered simply creating a new array from the existing value on the relay, appending, then calling accept?

myFilter.accept(myFilter.value + [newModel])

Building on Dalton's answer, here is a handy extension:

extension BehaviorRelay where Element: RangeReplaceableCollection {
    func acceptAppending(_ element: Element.Element) {
        accept(value + [element])
    }
}