Monks of the Expressors of Agape with Compassion will typically study several 'dead' religions* during their training and are encouraged to keep up devotions to those gods (this may also include other types of religion without gods as such). This is completely separate from their duties to the order and their Divinity.
The monk is not a full-time follower or devotee of any deity in his personal pantheon, and will not accept orders from them (they must go through the organisation like anybody else if they want to hire a monk), but he will worship each of them individually, roughly once a week.
The form of gift or ritual depends on the god, though the order forbids blood sacrifice (anything more than a token drop) and various other unsavoury practices; the deity must make do with whatever alternatives it's offered. The order has an almost patronising attitude to their small gods.
Weft has described his personal pantheon [1], which includes five original members and one that was assigned to him in later life:
* Ancient religions or religions with no known members left.