こんな感じか

function nextDate(x) {

switch (x.constructor) {
case Date: return NextDate(x)
case Number: return NextDate(x).getTime()
case String: return NextDate(x).toString()
default: throw "type err"
}

function NextDate(x) {
var date = new Date(x)
date.setDate(date.getDate() + 1)
return date
}

}