The phrase "more insensitive" is correct and usable in written English.
You could use the phrase "more insensitive" when someone has just said something offensive, and you want to emphasize that it was even more inappropriate than one might expect. For example: "His remark was already offensive, but then he added something even more insensitive."
Sarah is even more insensitive and self-absorbed than Elaine was on "Seinfeld".
It's less paternalistic than before, and generally speaking, a lot more insensitive.
With every day that passes, David Blunkett becomes more insensitive in his language and more intemperate in his actions.
I have rarely seen two more insensitive sentences: "Baghdad has weathered invasion, occupation, sectarian warfare and suicide bombers.
The cement-based modified soil with metakaolin was more insensitive to water and more convenient in the field rolling compaction.
Traditionally, she said, the biggest spenders -- those buying Park Avenue triplexes or Duane Street luxury lofts -- "were more insensitive" to the fluctuations of the economy as a whole.
Meanwhile, he's unafraid to have some of his more insensitive ideas backfire on him, such as adopting a child soldier for protection.
It can also demonstrate that the high-pressure turbine (HPT) power output is more insensitive to SEV fuel flow than the low-pressure turbine (LPT) one.
Telling people who are barely getting by that the economy is just fine must appear much more than insensitive.
For Nehru and the Congress Party's high command, such unilateral declarations were viewed as more than insensitive British behaviour, for, in undertaking to run most of British India's provinces, the Congress thought of itself as the viceroy's "partner" in administering the raj.
Consumers with high innovativeness, involvement, and loyalty are relatively more price insensitive than other consumers (Ramirez and Goldmith 2009; Goldsmith et al. 2010).
