Hello ran_d0m (if that is your name :P),
It is very consistent that there is only hardware to support one simultaneous connection over BLE with another BLE device on the cypress chips. See FAQ question "Can a Master connect to multiple Slaves?" answer: http://www.cypress.com/documentation/frequently-asked-questions/ble-frequently-asked-questions
There is the ability to broadcast unconnectable, undirected advertisements while connected to a single device, but only one physical hardware connection is allowed.
I believe some of the newer chips like the PSoC 6 might contain more hardware and potentially allow more connections at a time, but otherwise you are stuck doing it at the application layer to either: Make the device seem like it is connected to multiple at the same time, buffer data so you don't need to be, or change your application structure to be tolerant of only one connection at a time.
tl;dr; No, you can't have multiple BLE connections at the same time.