Adding contact on group messages and the option to add contact doesn’t show

Add or remove someone from a group conversation

Anyone in a group iMessage can add or remove someone from the conversation. You can remove a person from a group iMessage that has at least three other people. You can’t add or remove people from group MMS messages or group SMS messages.

Types of group messages

The three types of group messages that you might see are: group iMessage, group MMS, and group SMS. The Messages app automatically chooses the type of group message to send based on you and your recipients' settings, network connection, and carrier plan. For example:

• If you and your recipients are using Apple devices and iMessage is turned on, then the group message is sent as an iMessage.
• If you send a group message to people who aren't using iMessage, then the message is sent as an MMS or SMS message.

Do more with Messages

• Learn how to leave a group message, or add or remove someone from a group.
• Name your group messages to make them easier to find.
• Use inline replies and mentions to call attention to specific messages and people in your group messages.
• Explore the latest features in Messages to stay connected to the conversations that matter the most.

Bfrnk wrote:

How do I add a contact to group messages when the option ‘add contact’ doesn’t show

You don't, as you're in a group MMS, create a new thread and include the new contact.

You can only add in a group imessage.