So first we must identify the problem.
The problem is over-crowding. A combination of poor roads (particularly South/ANZAC Hwy at the moment), good publicity (do your bit for the environment) and service improvements (now takes you all the way to where you want to go) has left the tram system overwhelmed and under prepared.
What is the solution?
Make the trams longer (they're not linkable, but the government is allegedly looking into how to lengthen them) or get more trams (at present not possible because boom gates are not allowed to be down more than they already are).
The first is obvious and should be taken care of as a matter of urgency. Additionally, Memo Ministry of Tranport: all future trams must be couplable, as this makes life much easier for everyone.
The second is more interesting. It suggests a natural limit to services. But this is a fallacy: it just means that the tram must be, as far as possible, which is to say completely, independent of the road system. No major road should have a level crossing, and minor roads should be either blocked, or the government should accept that during peak hour, the boom gates will be down more often than not. If the trams were separated from Morphett Rd and others, it could cross there almost permanently during peak hour without disrupting the traffic flow along those other roads.
In summary, the short-term solution to tram overcrowding is to lengthen the trams. In the long term, the government must make a point of completely separating the rail and road transport systems so that the two can operate independently, and increase frequency of train services. This means an expensive infrastructure development programme, dotting Adelaide with under- and overpasses. Another major problem is the Park Tce level crossing on the Grange/Outer Harbour routes.
Fix it now, Minister Conlon!