Script to produce all combos (including empty) of a set of items. A bit clunky since PS tries to be helpful, but that doesn't play well when returning lists of lists.

Get-AllCombos.ps1

function Get-AllCombos {
    [CmdletBinding()]
    [OutputType("System.Collections.Generic.List[System.Object]")]
    Param (
        [Parameter(Mandatory)]
        [AllowEmptyCollection()]
        #[System.Collections.Generic.List[System.Object]]$arr
        [System.Collections.Generic.List[System.Object]]$arr
    ) 
    $ErrorActionPreference = [System.Management.Automation.ActionPreference]::Stop
    write-verbose $arr.Count -Verbose
    if ($arr.Count -eq 0) {
        return ,$arr
    }
    $lastIndex = $arr.Count-1
    $last = $arr[$lastIndex ]
    $arr.RemoveAt($lastIndex)
    [System.Collections.Generic.List[[System.Collections.Generic.List[System.Object]]]]$newCombos = Get-AllCombos $arr
    foreach ($combo in $newCombos) {
        $newCombo = [System.Collections.Generic.List[System.Object]]::new()
        $newCombo.Add($last)
        $newCombo.AddRange($combo)
        ,$combo
        ,$newcombo
    }
}

$array = @('a', 'b', 'c', 'd')
[System.Collections.Generic.List[[System.Collections.Generic.List[System.Object]]]]$results = Get-AllCombos $array
foreach ($x in $results) {
    $x -join ','
}