You can sort of do this today with some minimal customization:
Create an "Interesting Moments History" field (text field, not string). Then include an additional flow step (#3 in the screenshot below) within each IM trigger campaign that you want to include in the history field:


NOTE: We also increment an IM score field as part of this process.
The full value of the concatenated field is as follows:
{{lead.Last Interesting Moment Date}}: {{lead.Last Interesting Moment Desc}}{{my.line-break}}{{lead.Avanade Interesting Moment History}}
And the "line-break" token that's used is achieved by using @Sanford Whiteman's approach, documented here:
http://blog.teknkl.com/dark-mkto-alleys-line-break-token/ (don't be intimidated by the amount of detail here; as long as you follow the step-by-step instructions, it's actually very easy to implement. Also, we implemented this at the folder level of all of our operational programs/campaign - which enables you to only create this once and use the {{my.line-break}} token in as many programs/campaigns within that folder).
You can now insert the {{lead.Interesting Moments History}} field as a token in your alerts.