The short answer is 'Yes'.
The $ky Digibox points at Astra 28.2 East, it can get channels other than the pre-programmed ones but it cannot cope with some of the frequencies or 'symbol rates'.
So, to get the other channels, you'd need a general-purpose satellite receiver, known as a FTA receiver (Free-To-Air). These usually have a 'pass-through' connector to allow two tuners use the same dish.
BUT, there are probably very few channels on Astra at 28.2 East that cannot be received with the $ky box, so it might not be worth the bother.
You could motorise the dish so that it can point at other satellites or you could add another LNB so that it points at another satellite (e.g. Astra 19.2e or HotBird 13e). You'd definitely need to use the FTA receiver to control this and tune the non-$ky channels. The $ky box cannot do this.
Have a look at
www.lyngsat.com, check out what's free, what's on satellites that you can 'see' and what interests you.
If you do not want to pay for $ky & get their channels, you can get all the free BBC and ITV channels by connecting the FTA receiver to the same dish you were using for $ky & just put the $ky box away. You cannot get C4 or RTE TV with a FTA receiver.