Yes, enterprises can send multiple WhatsApp template messages outside a customer care session. These can be sent as part of business-initiated conversations. However, As of June 1, 2023, the business-initiated conversation category has been split into three new categories (each with their own pricing structure): utility, authentication, and marketing conversations. All templates used to begin business-initiated conversations will be associated with one of those three categories, and all of the above-mentioned conversations will still last 24 hours.
If you send a template message, and an existing conversation in the template message's category does not already exist, a new conversation will start. If you send a template message while there is already a conversation in progress, and the category of the template and the category of the open conversation do not match, a new conversation will begin in the category of the template. Finally, any template messages sent during a service conversation (referred to as a user-initiated conversation prior to June 1, 2023) will begin a new conversation in the category associated with the template.