@twilio/conversations connected but forbids adding new participants

I am using the @twilio/conversations library in a NextJS + React application. After successfully connecting with an Access Token, I am able to interact with the Client object normally and get participants, conversations, users, etc.

import { Client } from "@twilio/conversations"

const client = new Client(token)

However, when I try to add a participant I am receiving a Forbidden error. The current authenticated user is already a part of the conversation. I am trying to add a different, second user to the conversation. It doesn't matter which conversation or which user I attempt to add as a participant, the error is the same.

const conversation = await client.getConversationByUniqueName(conversationUniqueName)
const res = await conversation.add(userIdentity)

Error response:

Uncaught (in promise) Error: Forbidden
    at Upstream._callee$ (browser.js?5550:2968:1)
    at tryCatch (regeneratorRuntime.js?6f37:86:1)
    at Generator.eval [as _invoke] (regeneratorRuntime.js?6f37:66:1)
    at Generator.eval [as next] (regeneratorRuntime.js?6f37:117:1)
    at asyncGeneratorStep (asyncToGenerator.js?8e4b:3:1)
    at _next (asyncToGenerator.js?8e4b:25:1)