Various scientific studies have controlled for reach, frequency of exposure and media power to assess this effect. Here are links to some of them:

Lim et al., 2015 - multiple channels boost brand building. Also Voorveld, Neijens & Smit (2011).

Huang, 2016 - strong effect for unfamiliar brand.
​
Appleton-Knapp, Bjork & Wickens, 2005 - creatives need to be easy to connect. 
Unnava & Burnkrant (1991) - multiple creatives within a channel boosts brand building (also thought to be due to encoding variability).

​This LinkedIn post has a discussion of the topic.