Function overloading in PowerShell

In PowerShell functions are not overloaded. The last definition overrides the previous in the same scope or hides the previous in a parent scope. Thus, you should create a single function and provide a way to distinguish its call mode by arguments.

In V2 you may use an advanced function, see help about_Functions_Advanced_Parameters and avoid some manual coding on resolving parameter set ambiguities:

# advanced function with 3 parameter sets
function Backup-UsersData
(
    [Parameter(Position=0, ParameterSetName="user")]
    [string]$user,
    [Parameter(Position=0, ParameterSetName="array")]
    [object[]]$array,
    [Parameter(Position=0, ParameterSetName="all")]
    [switch]$all
)
{
    # use this to get the parameter set name
    $PSCmdlet.ParameterSetName
}

# test
Backup-UsersData -user 'John'
Backup-UsersData 1, 2
Backup-UsersData -all

# OUTPUT:
# user
# array
# all

Note that this mechanism is sometimes strange. For example in the first test we have to specify parameter name -user explicitly. Otherwise:

Backup-UsersData : Parameter set cannot be resolved using the specified named parameters.
At C:\TEMP\_101015_110059\try2.ps1:21 char:17
+ Backup-UsersData <<<<  'John'
    + CategoryInfo          : InvalidArgument: (:) [Backup-UsersData], ParentContainsErrorRecordException
    + FullyQualifiedErrorId : AmbiguousParameterSet,Backup-UsersData

In many cases standard, not advanced, function with mixed parameters will do:

function Backup-UsersData
(
    [string]$user,
    [object[]]$array,
    [switch]$all
)
{
    if ($user) {'user'}
    elseif ($array) {'array'}
    elseif ($all) {'all'}
    else {'may be'}
}

Backup-UsersData -user 'John'
Backup-UsersData -array 1, 2
Backup-UsersData -all
Backup-UsersData

But in this case you should resolve (or accept and ignore) ambiguities, e.g. to decide what to do if, say:

Backup-UsersData -user 'John' -array 1, 2 -all

Here is a variant of Roman's answer that I think is a little more flexible:

function Backup
{
    [CmdletBinding(DefaultParameterSetName='Users')]
    Param (
        [parameter(mandatory=$true, ParameterSetName='Users', position=0, ValueFromPipeline=$true)][string[]]$User,
        [parameter(mandatory=$true, ParameterSetName='AllUsers')][switch]$All
    )

    Begin
    {
        if ($All) { $User = @('User1', 'User2', 'User3') }
    }

    Process
    {
        foreach ($u in $User)
        {
            echo "Backup $u"
        }
    }
}

1) Build a class...

class c1 { 
    [int]f1( [string]$x ){ return 1 } 
    [int]f1( [int ]$x ){ return 2 }
    }

1+) Use STATIC METHODS if you prefer to call them without instantiation...

class c1 { 
    static [int] f1( [string]$x ){ return 1 } 
    static [int] f1( [int]$x ){ return 2 } 
    }

2) Call the methods in class or object... overload works OK

$o1 = [c1]::new()
o1.f1( "abc" ) ~> returns 1
o1.f1( 123 )   ~> returns 2

---

-OR-

---

[c1]::f1( "abc" ) ~> returns 1
[c1]::f1( 123 )   ~> returns 2

3) If (like me)
you want to have "Overloaded Functions" placed in a libraries...
so your users can use them transparently...
from code or from Interactive Command Line (REPL)...

the closest I could came to
"Overloading functions in Powershell"
was something like this:

function Alert-String() { [c1]::f1( "abc" ) }
function Alert-Strings(){ [c1]::f1( 123 ) }
function Alert-Stringn(){ [c1]::f1( 123 ) }

Maybe in PS-Core v8??? ;-)

Hope it helps...