Well, what the Byzantines have are Liturgies of Presanctified Gifts, which are usually held during days of abstinence, as a reminder of the Divine Lord's repentance and giving His life for those during this solemn period of the year, now I know this is different from the Divine Liturgy, but it still does give us that "more than one service than just Sundays" during this period. These are usually commonplace during the Great Fast season. Also, on weekends, the Divine Liturgy of St. Basil is held in place of the usual St. John Chrysostom Divine Liturgy. I hope that answers a few of the questions you might have about that.
Now for the Oriental Orthodox and Catholics, that I cannot really be certain of. One can assume they hold different services of repentance and reminder of the season. Whether they usually hold a Vespers service of sorts during the week, or whether they do hold some Liturgical services, I have to ask one of my friends of the Coptic Orthodox faith on that one when I meet him again during their summer Egyptian Festival.
