Conversational systems can be particularly effective in supporting complex information seeking scenarios with evolving information needs. Finding the right products on an e-commerce platform is one such scenario, where a conversational agent would need to be able to provide search capabilities over the item catalog, understand and make recommendations based on the user's preferences, and answer a range of questions related to items and their usage. Yet, existing conversational datasets do not fully support the idea of mixing different conversational goals (i.e., search, recommendation, and question answering) and instead focus on a single goal. To address this, we introduce MG-ShopDial: a dataset of conversations mixing different goals in the domain of e-commerce. Specifically, we make the following contributions. First, we develop a coached human-human data collection protocol where each dialogue participant is given a set of instructions, instead of a specific script or answers to choose from. Second, we implement a data collection tool to facilitate the collection of multi-goal conversations via a web chat interface, using the above protocol. Third, we create the MG-ShopDial collection, which contains 64 high-quality dialogues with a total of 2,196 utterances for e-commerce scenarios of varying complexity. The dataset is additionally annotated with both intents and goals on the utterance level. Finally, we present an analysis of this dataset and identify multi-goal conversational patterns.