For troparia, three's the limit at Vespers and Matins (at Vespers this includes a theotokion, at Matins an additional theotokion may also be included to make four). Two troparia are the max for each of the Little Hours.
Compline is more variable; in some rules troparia are mentioned and some kontakia, some both, and up to four or more may be instructed to be taken (day, feast, patron, saint(s) of the day, etc) at Compline.
For kontakia, at Matins two, one after Ode 3 and one after Ode 6 (but several can be aggregated after Ode 3); and for kontakia at the Little Hours only one is taken per hour.
The Divine Liturgy is another thing entirely, and one often sees aggregations of troparia and kontakia not seen to that degree in any of the Divine Praises.
In our Blessed Isidore Dolnytsky's Typikon for the UGCC, he prescribes the separation of troparia and kontakia throughout the Little Hours to "cover the bases" on non-polyeleos weekdays. So at the first hour you take the daily commemoration (based on day of the week), at the third and ninth the saint(s) of the day (separate kontakia and troparia at each if mutiple saints are commemorated) and at the sixth the patron of the temple.