"investigate it further" is a grammatically correct and usable phrase in written English. You can use it when you want to suggest that someone look into a particular issue or subject with more depth or detail. For example, "We only have the basic information about the project so far. Let's investigate it further and see what else we can find out.".
If the event is rare we may decide, based on its occurrence probability, to investigate it further or not.
Interestingly, DDP1 has previously been shown to play a role in centromeric silencing [46], [47], but we decided not to investigate it further, due to the lack of its kinetochore localization.
Sedikides decided to investigate it further.
"We need to investigate it further," Dr. Stöhr said.
Parker: We never really investigated it further.
The United States Coast Guard said it found no pollution as a result of the incident, but was investigating it further.
"The principal checked it out, and then we investigated it further".
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Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia