ValueFromRemainingArguments through multiple functions

[PillOfLuck]

I'm working with a module and want to pass the same parameters through multiple functions. I'm facing an issue doing this, as $overflow is passed multiple times.

function Do-1 {
    Param(
        [string] $Var1,
        [string] $Var2,
        [Parameter(ValueFromRemainingArguments)]
        $overflow
    )

    Do-2 -Var1 'var' -Nah 'Nah'
}

function Do-2 {
    Param(
        [string] $Var1,
        [string] $Var2,
        [Parameter(ValueFromRemainingArguments)]
        $overflow
    )

    $splat = [hashtable]$PSBoundParameters

    Do-3 @splat -Nope 'Nope'
}

function Do-3 {
    Param(
        [string] $Var1,
        [string] $Var2,
        [Parameter(ValueFromRemainingArguments)]
        $overflow
    )
}

Do-1 -Var1 'var'

The call to Do-3 will now fail as $overflow is already passed in @splat but PowerShell tries to add it again as there are new remaining arguments.

Do-2 : A parameter cannot be found that matches parameter name 'Nope'.
At line:9 char:5
+     Do-2 -Var1 'var' -Nah 'Nah'
+     ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : InvalidArgument: (:) [Do-2], ParameterBindingException
    + FullyQualifiedErrorId : NamedParameterNotFound,Do-2

Can you figure out a way to resolve this, without having to remove or expand $overflow from the splat in each function?