BindMind's page

Guess what are you looking for is the splinter faith class feat.

And that feat, apart from being extremely rare and not usable without DM permission, explains in a proper way what you are talking about ( having more than 1 deity).

Finally,I think that it's implicit that a cleric would also become a champion of the same deity ( the dedication is probably that detailed for no cleric/champions).

I'm not so sure about this one. Splinter Faith reads the following way:

Your faith in your deity is represented in an extremely unusual way that some might call heretical.

The feat calls out an unusual way of following a specific deity. It makes no mention of following a second deity and following its tenets in tandem with the first deity. The archetype definitely reads more like Syncretism to me:

You have come to see the overlap between two deities’ teachings. Choose a second deity. You must meet their alignment requirements, and you are subject to their edicts and anathema.

The archetype basically reads the same way, with the exception of not explicitly calling out "second" deity.

I have a player who is archetyping into Champion as a Cleric, and this rules question came up (more out of curiosity than anything).

The Cleric reads the following way:

As a cleric, you are a mortal servitor of a deity you revere above all others.

So we pick a deity. Then, we archetype into Champion, which reads:

Choose a deity and cause as you would if you were a champion.

Which refers to the Champion:

Champions are divine servants of a deity. Choose a deity to follow; your alignment must be one allowed for followers of your deity.

Now as far as I can tell, the archetype makes no mention of the deity having to be the same as the one you wrote in the "deity" box on your character sheet. However, the "Deity" section throws a wrench in this somewhat:

Write down the deity your character worships, if any. Champions and clerics must worship a deity. See pages 437–440 for more about Pathfinder’s deities.

This explicitly calls out "the deity", not "the deities". However, this is a general rule, and doesn't explicitly put a limiter on your deity count. As with Syncretism (Gods & Magic pg. 105), where you can select a second deity (where the specific rule overrides the general), I would assume since the archetype gives you an additional "choose", you are not forced to choose the same deity as a Champion as you did as a Cleric.

I was curious as to what the general consensus on this was, or at the least what people's thoughts were. I would say as a GM you simply treat the classes separately, where breaching anathema set by your Cleric side locks you out of Cleric stuff but not your Champion stuff, and vice versa. However, there could be something I missed here.