In Odoo 15 I have to override _search methdo from js backend.

This way worked for me:

Create a fields.js file with:

/* Override Search More ... option in Many2one fields */
odoo.define('my_module.Fields', function (require) {
"use strict";

var relational_fields = require('web.relational_fields');
var FieldMany2One = relational_fields.FieldMany2One;

FieldMany2One.include({
_search: async function (searchValue = "") {
const value = searchValue.trim();
const domain = this.record.getDomain(this.recordParams);
const context = Object.assign(
this.record.getContext(this.recordParams),
this.additionalContext
);
var values = await this._super.apply(this, arguments);

// Add "Search more..." option even if results count is lower than the limit of 7
if (this.limit >= values.length) {
values = this._manageSearchMore(values, value, domain, context);
}

return values;
},
})
});

Then add this line to __manifest__.py

'assets': {
'web.assets_backend': [
'my_module/static/src/js/fields.js',
],
},