I am using Jmeter 5.2.1. While recording the script due to the heavy response, body data is not recorded properly and due to this when I tried to modify the ids at that time its request failed.
In addition, I also tried the same with the BlazeMeter chrome extension but the result is the same.
Is it possible to increase the size of the body data or any other possible way to manage these types of requests at recording time?

"Not recorded properly" shouldn't be the case, the request is either recorded or not. If JMeter fails to capture the request body fully it shouldn't create the relevant HTTP Request sampler. And also JMeter should print some information on the problem to jmeter.log file.
So my expectation is that you're introducing the "problem" when you're "trying to modify the ids"
If it's really a JMeter problem you should raise an issue so developers and maintainers could fix it. In the meantime you can use the following workarounds:
Use your browser developer tools or 3rd-party sniffer tool like Fiddler or Wireshark to capture particular this request (or the whole test scenario)
You can use i.e. BlazeMeter Converter to transform captured requests into .jmx script.
Try upgrading to the latest stable version of JMeter which is JMeter 5.5 as of now because it's recommended to use the latest version.