In Vue.js, how can I emit multiple value from child to parent while parent’s v-on pass another parameter?

Define a handler that accepts the multiple parameters from the event and passes them along to the change method in addition to your static parameter.

<button-counter v-on:change="(...args)=>this.change(1234,...args)"></button-counter>

Alternatively

<button-counter v-on:change="(...args)=>this.change([1234,...args])"></button-counter>

And change your method to

change: function (args) {
  this.args = args
  console.log(args)
}