You can run out of sensible things to do, the ability to supply adequate power, or money before there is a structural problem. I have seen an arduino that was about fifty stories high. I have no idea of what it did - impress the natives, I suppose.
There is more than one way for pins to be shared and many, indeed usually most, pins on shields are pass through and unused thereon. That is how the system works. A specific example is the SPI bus, which uses pins 10>13, and what Weed is saying about pins 10>13 specifically, is nonsense.
The pic below is a four storey arduino. It is actually shown on a Mega, but they started out on a Uno. Next up is a commercial ethernet shield which uses SPI, pins 10>13, and has an SD card on board. The next, barely visible, is a sensor shield and has a clock which, on a Uno, is connected to the I2C bus on pins A4,5, which pass though the ethernet shield but are unused by it. Here on the Mega, the clock is connected to pins 20,21 by a flying lead. The top shield is just the display, which is also on the SPI bus, pins 11>13. The SPI pins are just pass-through on the sensor shield but shared with ethernet, and the LCD has its exclusive select pin 7.
The bluetooth is just a breakout board with a flying lead to the sensor shield. A bluetooth shield could join the rest, and just use pins 0,1, which are unused by any of the others.
Note that there are differences between Mega and Uno in the allocation of pins for the SPI bus. This is not a problem, and the most common shield using it, the ethernet cum SD shield, fits both.