How many times in one day may a layman receive Holy Communion? For instance, if someone were to attend a morning Mass and receive Holy Communion then, would it be acceptable or not to receive Holy Communion at a later Mass in the afternoon?

This is an easy question. Clear-cut, Church teaching, not a disputed question OR matter of opinion. I'll also point out: I speak for the Church here. This is not my opinion. This is Traditional, pre-Vatican II Catholic teaching.

You may only receive Holy Communion ONCE per day.

The only exception is if you are in danger of death. Even if you went to morning Mass and received, and then found yourself in danger of death later that day, you could receive Viaticuм from a priest.

In short, Viaticuм doesn't count towards your "one Holy Communion per day".

Here is the reference, Vermont:
“ 700. No one is allowed to receive holy Communion a second time on the same day, except in the cases mentioned in Canon 858, 1. (Canon 857.) Cf. Canon 864, 2. 701. Those who have not kept the natural fast from midnight are not allowed to receive, except in danger of death, or in case it should become necessary to consume the Blessed Sacrament to safeguard it against irreverence. The sick who have been laid up for a month without certain hope of speedy recovery, may, with the advice of the confessor, receive holy Communion once or twice a week though they have taken medicine or some liquid food. (Canon 858.)”