Time Series with Multiple Intervention Dates

I'm working with a time series in which the same intervention was applied to a large number of items but at different points. Essentially, I have figures by day (and can roll them up by week, month, etc.) and I am trying to figure out what the impact of the intervention is on the figures. The table looks like this.

Date1 Date2 Date3 Date4 Date5 Date6 DateX.... InterventionDate
1.2 1.4 2.5 3.6 1.5 1.3 1.7 2/14/2015
2.1 1.3 5.6 1.2 1.5 2.1 0.9 1/2/2015

All the time series intervention analyses that I'm familiar with (ARIMA, Google's CausalImpact, etc.) rely on the intervention date being a fixed point that is in common across all the data points. In a case like this where the intervention dates vary for each data point, is there a time series model that I can use to determine the impact of the intervention?