You can add multiple custom fields to JIRA Service Desk customer portal and JIRA issue create/view/edit screens. Each custom field may contain different form assets.
For more information on adding custom fields, please see official Atlassian documentation.
To create a custom field in JIRA please follow these steps:
Configure the selection criteria for the field.
Enter Name for this custom field. For example: Server Assets.
Select the checkboxes of the screens on which this custom field will be displayed.
New custom field is ready to use. By default it display all the assets of the system. You can limit the forms in Assets configuration page: