Can incubation be facilitated, while, at the same time, being focused on a different problem? Is it possible to facilitate incubation as well as consciously think about a different problem at the same time, in effect multitasking, in order to gain insights more quickly, without having to stop and take a break. 

For context, see this question on incubation:

How is it that taking a break from a problem sometimes allows you to figure out the answer?
This is an interesting question because it relates to different mechanisms that may be responsible for incubation effects: 


Does incubation occur because creative insight is helped by unconscious processes? (Processes that are best left undisturbed by not consciously thinking about the problem?) In this case, the most important thing would be to focus on something else.
Or does taking a break simply reduce mental fatigue as some have claimed (e.g., Posner, 1973, as cited in Sio &amp; Ormond, 2009)? In this case, just taking a break from thinking might be best.
Or is it because of certain patterns of conscious thought during incubation? In this case, the kind of problem one thinks about consciously during the incubation phase would matter.


Sio and Ormond (2009) have looked at this question as part of their meta-analysis of incubation studies: 


They found that performing low cognitive demand tasks were associated with stronger incubation effects than just taking a break and doing nothing
However, high cognitive demand tasks were associated with smaller incubation effects


These results are not in line with a simple mental fatigue account of incubation. Instead, they suggest that creative insight profits more from distracting tasks that are low in cognitive demand.

One explanation for these findings is that low demanding tasks allow and promote mind-wandering (Baird et al., 2012).

Conclusion: So based on this research, when trying to generate some creative insight, it might be good to take a break after an intense preparation period. However, instead of occupying your mind with another hard nut to crack, it might be better to do so with something that is not very demanding. Try cleaning up your desk and water those sad-looking plants in your office!

References

Baird, B., Smallwood, J., Mrazek, M. D., Kam, J. W. Y., Franklin, M. S., &amp; Schooler, J. W. (2012). Inspired by distraction: Mind wandering facilitates creative incubation. Psychological Science, 23, 1117–1122. doi:10.1177/0956797612446024

Sio, U. N., &amp; Ormerod, T. C. (2009). Does incubation enhance problem solving? A meta-analytic review. Psychological Bulletin, 135, 94–120. doi:10.1037/a0014212