No, vue doesn't work with a direct inheritance model. You can't A.extend an component, as far as I know. It's parent-child relationships work mainly through props and events.
There are however three solutions:
1. Passing props (parent-child)
var SomeComponentA = Vue.extend({
    methods: {
        someFunction: function () {
            // ClassA some stuff
        }
    }
});
var SomeComponentB = Vue.extend({
   props: [ 'someFunctionParent' ],
   methods: {
       someFunction: function () {
           // Do your stuff
           this.someFunctionParent();
       }
   }
});
and in the template of SomeComponentA:
<some-component-b someFunctionParent="someFunction"></some-component-b>
2. Mixins
If this is common functionality that you want to use in other places, using a mixin might be more idiomatic:
var mixin = {
    methods: {
        someFunction: function() {
            // ...
        }
    }
};
var SomeComponentA = Vue.extend({
    mixins: [ mixin ],
    methods: {
    }
});
var SomeComponentB = Vue.extend({
   methods: {
       someFunctionExtended: function () {
           // Do your stuff
           this.someFunction();
       }
   }
});
3. Calling parent props (parent-child, ugly)
// In someComponentB's 'someFunction':
this.$parent.$options.methods.someFunction(...);