Dragon Slayer magic was a rare type of magic. I doubt there would be more dragon slayers other than those already introduced. Also to be noted is that only dragon slayers taught by dragons have Exceed partner.
Natsu Dragneel was taught by Igneel. Partner Happy.
Gajeel Redfox was taught by Metallicana. Partner Pantherlily.
Wendy Marvell was taught by Grandine. Partner Carla.
Sting was taught by Weisslogia. Partner Lector.
Rogue was taught by Skiadrum. Partner Frosch.
Other dragon slayers who became one due to lacrima being embedded into them don't have Exceed partner.
Laxus Dreyar, thunder dragon slayer.
Cobra, poison dragon slayer.
God Serena, multiple element dragon slayer.
Another thing that they have in common is that all dragon slayers with Exceed patners all was sent into the present from the past using the Eclipse gate.
Thus, if we go by this pattern, the other Exceed (of those sent to Earth) are all partnerless because in the present dragons have already go extinct, with the exception of Acnologia. Only 5 dragon slayers were sent from the past and all those 5 have their partners already.
Acnologia was originally a human taught by a dragon. In this sense he is the same as the other 5. However, he is never seen with an Exceed partner. It is safe to assume that he don't have one.
As for whether there are more dragon slayers than currently shown, we can't say for sure because the story still goes on.