You have two options as ASME 31E said, one is three directional excitations such as plant east-west, north-south and vertical, with the combination of square-root sum of the squares (SRSS) or two directional
design approach of based on the envelope of SRSS of east-west plus vertical and north-south plus vertical seismic loadings.
According to this definitions, the former is as follows if X is east-west direction and Y is vertical with the maximum design acceleration being 0.3 in horizontal and a half in vertical:
E1: 0.212 0.0 0.0...X direction
E2: 0.0 0.15. 0.0...Y direction
E3: 0.0. 0.0 0.212...Z direction
And E1+E2+E3 by load combination done by SRSS.
The latter is as follows:
E1: 0.3. 0.0 0.0
E2: 0.0 0.15. 0.0
E3: 0.0. 0.0 0.3
And E1+E2 or E2+E3 with load combination done for each case by SRSS.
Then the maximum is selected from these two cases for each evaluation node.
Also if the gap or lift-off is to be considered in piping system, you should add positive and negative direction for each X, Y and Z direction with normal operating condition such as W+T1+P1, that means W+T1+P1+E1, W+T1+P1+E2 and W+T1+P1+E3 for judging those nonlinear support conditions and after that you can get occasional load effect.