Take a look in the documentation for 'inherited view', that will allow you to expand the base.view_partner_tree.

Be sure that your field are not already present but in invisible='1' (eg: user_id, is_company, country_id, parent_id, active)

Here, a short example:

    <record id="view_res_partner_inherit_tree" model="ir.ui.view">
        <field name="name">res.partner.inherit.tree</field>
        <field name="model">res.partner</field>
        <field name="inherit_id" ref="base.view_partner_tree"/>
        <field name="arch" type="xml">
            <field name="user_id" position="after">
                <field name="my_new_field"/>
                <field name="another_new_field"/>
            </field>
        </field>
 </record>