'further tap into' is correct and usable in written English.
It is often used to refer to exploring deeper into a topic or idea. For example, "The conference provided an opportunity to further tap into our knowledge of the subject."
In the 90's, with the success of "Def Comedy Jam," the Big Three networks decided it was time to further tap into the black audience.
To achieve this one might further tap into recent ideas for classifying emergent dynamics based upon the group of structural symmetries of the network.
Google has begun to further tap into the power of the crowd in order to improve its Google Maps application, the company announced this morning.
Edouard de Witte, Deputy Director at RTL Newmedia says "Adding radio and mobile technology platforms to the mix enables us to further tap into the full potential this type of unobtrusive ad serving offers".
After Umuntu took off in web and mobile form, Mr Nel had a vision to use it as a springboard to further tap into mobile e-commerce with the creation of the mobile site, Mimiboard, which has been live for a month.
This excitement is something that Democrats would be wise to further tap into and grow.
— and revolution brews, Ireland further taps into the anger that can be found in Marie's shrillness.
In narrating Derek's buried crime story, Pelecanos has further tapped into an archetypal vein of family experience in the black community since the 1950's, as drugs, murder and prison cut a swath through three generations of young men.
In some ways, Tencent's credit system goes further, tapping into users' social networks and mining data about their contacts, for example, in order to determine their social-credit score.
Myog-deleted mice display increased levels of lactate build-up at exhaustion and are capable of further tapping into glycogen stores that wild-type mice do not access before reaching exhaustion.
Improved fat burning means endurance athletes can go further before tapping into carbohydrate stores.
