We present a computational modelling approach which targets capturing the specifics on how to virtually augment a Metaverse user's available social time capacity via using an independent and autonomous version of her digital representation in the Metaverse. We motivate why this is a fundamental building block to model large-scale social networks in the Metaverse, and emerging properties herein. We envision a Metaverse-focused extension of the traditional avatar concept: An avatar can be as well programmed to operate independently when its user is not controlling it directly, thus turning it into an agent-based digital human representation. This way, we highlight how such an independent avatar could help its user to better navigate their social relationships and optimize their socializing time in the Metaverse by (partly) offloading some interactions to the avatar. We model the setting and identify the characteristic variables by using selected concepts from social sciences: ego networks, social presence, and social cues. Then, we formulate the problem of maximizing the user's non-avatar-mediated spare time as a linear optimization. Finally, we analyze the feasible region of the problem and we present some initial insights on the spare time that can be achieved for different parameter values of the avatar-mediated interactions.