The presence of white spaces and spectrum holes in the TV bands represents potential opportunities for alleviating the apparent spectrum scarcity. Opportunistic spectrum access (OSA) has been proposed for the secondary user's operation and the main concern is the harmful interference that secondary systems could cause to the primary receivers. Existing studies have focused on establishing the limits for co-channel and adjacent channel interference when only one adjacent channel is used by a single secondary user. This paper presents a characterization of the aggregate adjacent channel interference (AACI) when different adjacent channels are simultaneously accessed by multiple secondary users or white space devices (WSDs). An analytical expression is proposed to approximate the limits of the tolerable AACI. Our model states that not only the interference received in each adjacent channel should stay below the corresponding threshold for that particular channel, but also the weighted sum of the total adjacent channel interference power should be kept below a certain threshold. Measurement campaigns show the cumulative effect of the adjacent channel interference (ACI) when multiple WSDs access multiple adjacent channels at the same time. The proposed analytical expression for AACI closely matches the measurement results.