Is there a way to install both tabular and multidimensional modes? I have started studying for the MCSE BI exam. I would like to have both the multidimensional and tabular modes available for studying/practice purposes. I have a SQL Server 2014 Developer Edition with tabular mode installed.

Is it simply a matter of installing another named instance? Seems like there's a gotcha somewhere in there, but I have not found it in the research I have done so far.
You answered your own question. You simply install another instance of SSAS.