In the context of PHP form submissions, what are some alternative methods to using sessions for storing and maintaining values between multiple form submissions?

When working with PHP form submissions, an alternative method to using sessions for storing and maintaining values between multiple form submissions is to use hidden input fields within the form itself. By including hidden input fields with the desired values, the data can be passed along with each form submission without the need for sessions.

```php
<form action="process_form.php" method="post">
  <input type="hidden" name="hidden_field" value="<?php echo isset($_POST['hidden_field']) ? $_POST['hidden_field'] : ''; ?>">
  <!-- other form fields here -->
  <input type="submit" value="Submit">
</form>
```

In the above code snippet, a hidden input field is included within the form, which stores the value of 'hidden_field' from the previous form submission. This value will be passed along with each subsequent form submission, allowing for the data to be maintained without the need for sessions.