We studied the coronal mass ejections (CMEs) and flares associated with large solar energetic particle (SEP) events of solar cycle 23 (1996--2002) in order to determine what property of the solar eruptions might order the SEP intensity. The SEP events were divided into three groups: (1) events in which the primary CME was preceded by one or more wide CMEs from the same solar source, (2) events with no such preceding CMEs, and (3) events in which the primary CME might have interacted with a streamer or with a nearby halo CME. The SEP intensities are distinct for groups 1 and 2 although the CME properties were nearly identical. Group 3 was similar to group 1. The primary findings of this study are as follows: (1) Higher SEP intensity results whenever a CME is preceded by another wide CME from the same source region. (2) The average flare size was also larger for high-intensity SEP events. (3) The intensity of SEP events with preceding CMEs showed a tighter correlation with CME speed. The extent of scatter in the CME speed versus SEP intensity plots was reduced when various subgroups were considered separately. (4) The intensities of energetic electrons were better correlated with flare size than with CME speed. (5) The SEP intensity showed poor correlation with the flare size, except for group 3 events. Since only a third of the events did not have preceding CMEs, we conclude that the majority of SEP producing CMEs propagate through the near-Sun interplanetary medium severely disturbed and distorted by the preceding CMEs. Furthermore, the preceding CMEs are faster and wider on the average, so they may provide seed particles for CME-driven shocks that follow. Therefore we conclude that the differing intensities of SEP events in the two groups may not have resulted due to the inherent properties of the CMEs. The presence of preceding CMEs seems to be the discriminating characteristic of the high- and low-intensity SEP events.