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