A simple sample plugin / template plugin / demo plugin (mostly without Settings API) which creates a * Settings page in a Wordpress Network (WPMU).

sample-plugin.php

<?php
/**
 * Plugin Name: My Plugin
 * Plugin URI: 
 * Description: A simple sample plugin / template plugin / demo plugin (mostly without Settings API) which creates a
 * Settings page in a Wordpress Network (WPMU). 
 * Replace 'my_plugin' and 'my-plugin' with something that makes sense to you and you are set
 * Regex: replace my(.)plugin with really$1nice
 * Add some settings to default_settings (use underscores for values) and add descriptions in $this->decriptions
 * If you want a custion form-field: your_setting_form_callback($name, $value, $description)
 * Thanks to: https://samelh.com/blog/2017/02/19/add-wordpress-network-settings-page-plugin/
 * Author: Vitus Schuhwerk
 * Version: 0.01
 * Author URI: v-5.eu
 */

namespace MyPlugin\Admin;
$MyPluginAdmin = new \MyPlugin\Admin\Admin;
$MyPluginAdmin->init();


class Admin {

    public $errors;
    public $name = ''; //the plugin name, set in init
    public $default_settings = array(
        'setting_1' => '', //triggers setting_1_form_callback & setting_1_validate if exist
        'setting_2' => ''
    );
    public $descriptions = array(); //descriptions for settings
    public $prefix = 'my_plugin'; 
    public $optionname = 'my_plugin'; //also the name of the metakey
    public $slug = 'my-plugin'; //the plugin slug

    /**
      * register custom settings admin page
      */
    public function init(){
        $this->name = __('my plugin', 'my-plugin-domain');
        $this->descriptions = array(
            'setting_1' => __('my first description', 'my-plugin-domain'),
            'setting_2' => __('my second description', 'my-plugin-domain')
        );
        add_action('network_admin_menu', array($this, 'setup_submenu')); // register page
        add_action('network_admin_menu', array($this, 'update')); // update settings
    }

    public function setup_submenu(){
        add_submenu_page(
            'settings.php',
            sprintf(__('%s Settings', 'my-plugin-domain'), $this->name),
            $this->name,
            'manage_options',
            $this->slug,
            array($this, 'screen')
        );
        return $this;
    }

    public function setting_1_form_callback($name, $value, $description){
        //checkbox returns 1 if the value in the markup is set to 1
        $checked = checked( $value, 1, false); //check for 1 and don't echo
        return "
            <tr>
                <th>$description</th>
                <td>
                    <input type='checkbox' value='1' name='$name' $checked />
                </td>
            </tr>
        ";
    }

    public function get_default_field($name, $value, $description){
        return "
            <tr>
                <th>$description</th>
                <td>
                    <input type='text' name='$name' value='$value' size='50' />
                </td>
            </tr>
        ";
    }

    /**
     * Check if a function exists. $name is 'test' and $callback_suffix is
     * '_try'. if the function 'test_try' exitst in the class the function
     * returns 'test_try', otherwise false
     *
     * @param      <type>   $name            The name
     * @param      <type>   $calback_suffix  The calback suffix
     *
     * @return     boolean  ( the name of the function or false. don' forget $this-> when you call the funciton )
     */
    public function check_callback_name($name, $calback_suffix){
        $function_name = $name.$calback_suffix;
        if (method_exists($this, $function_name)){
            return $function_name;
        }
        else {
            return false;
        }
    }

    /**
     * Prints form fields. Checks for a callback like setting_1_form_callback.
     * If it does not exist it just creates a text field.
     *
     * @return     string  The fileds.
     */
    public function get_fileds(){

        $settings = wp_parse_args(
            get_site_option($this->optionname), 
            $this->default_settings
        );

        $fields = '';
        foreach ($settings as $name => $value) {
            $description = isset($this->descriptions[$name]) ? $this->descriptions[$name] : $name;
            $cb = $this->check_callback_name($name,'_form_callback');
            if ($cb){
                $fields .= $this->$cb($name, $value, $description);
            }
            else {
                $fields .= $this->get_default_field($name, $value, $description);
            }
        }
        return $fields;
    }

    /**
      * This method will parse the contents of
      * our custom settings age
      */
    public function screen(){ 

        $messages = settings_errors($this->prefix);
        echo "
            <div class='wrap'>
                <h2> $this->name </h2>
                $messages
                <form method='post'>
                    <table class='form-table'>"
                        .$this->get_fileds()
                        .wp_nonce_field('my_plugin_nonce', 'my_plugin_nonce', true, false).

                    "</table>
                    ".get_submit_button()."
                </form>
            </div>
        ";
    }

    /**
      * Check for POST (form submission)
      * Verifies nonce first then calls
      * update_settings method to update.
      */
    public function update() {
        if ( isset($_POST['submit']) ) {

            // verify authentication (nonce)
            if ( !isset( $_POST['my_plugin_nonce'] ) )
                return;

            // verify authentication (nonce)
            if ( !wp_verify_nonce($_POST['my_plugin_nonce'], 'my_plugin_nonce') )
                return;

            return $this->update_settings();
        }
    }

    public function setting_2_validate ($name, $value){
        if ($value == ''){
            add_settings_error(
                $this->prefix,
                'validationError',
                "$name is not supposed to be empty!",
                'error'
            );
        }
        return $value;
    }

    /**
     * Call function like setting_1_validate. If that fonction does not exist
     * the $_POST variable is directly saved.
     */
    public function update_settings() {
        $settings = array();

        foreach ($this->default_settings as $name => $value) {
            if(isset($_POST[$name])){
                $cb = $this->check_callback_name($name, '_validate');
                if ($cb){
                    $settings[$name] = $this->$cb($name, $_POST[$name]);
                }
                else {
                    $settings[$name] = $_POST[$name];
                }
            }
        }
        error_log(print_r($_POST, true));
        if ( $settings ) {
            // update new settings
            update_site_option($this->optionname, $settings);
        } else {
            // empty settings, revert back to default
            delete_site_option($this->optionname);
        }
        if (empty(get_settings_errors($this->prefix))){ //there are no errors
            add_settings_error(
                $this->prefix,
                'validationError',
                'Successfully updated settings :)',
                'updated'
            );
        }

    }
}