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Interstitial ≠ parallel

The difference between interstitial and parallel not to be confused. 
If we think of a managerial practice that tries to avoid schizophrenia; pick your bucket of obligations and liaise with them one by one. 

In this context to "run things in parallel" has to do with the ability of a subject to start and get involved in a variety of projects/obligations without terminating them as soon as they've been started. The key ability here is not only to focus, but to refocus; to be able to effectively shift between tasks. For this focusing can be productive in the realisation of a project but might be detrimental if the ability to shift is not exercised, as too much energy might go into solving this one problem and not addressing others, i.e. Having a "general picture". 

This shifting aims at a holism that requires a balance of parts, but not of all of them; rather of the relevant parts, which are paramount to monitor and keep an eye on. 
Keeping an eye on the matters to treat means an attention span that requires alertness throughout the day coupled with an availability of required materials. The identifying of functional or productivity gaps is enabled by this alertness which also makes sure that tools are at hand; i.e. Pen and a pencil, and makes use of this interstitial gaps in the working day. Then we can say we are making the most of the day by working continuously towards the achievement of a defined goal. This in-between time makes us works in parallel and serves to clean up or advance tasks that require imminent completion.