Hi DJ,
It depends on what you mean by sum. On a Bode plot gains are in dB, so summing is equivalent to multiplication of gains, which is a series connection for transfer functions. (Or multiplication in the s-domain.) Such multiplication also sums phase response. Below tf1 has DC gain 1 and a single pole at -10; tf2 has gain 2 and a pole at -1000; tfSum is the series connection.
tf1 = TransferFunctionModel[{{{{}}}, {{{-10}}}, {{1 10}}}, s]
tf2 = TransferFunctionModel[{{{{}}}, {{{-1000}}}, {{2 1000}}}, s]
tfSum = SystemsModelSeriesConnect[tf1, tf2]
BodePlot[{tf1, tf2, tfSum}, PlotLegends -> {"TF1", "TF2", "Sum"}]
