On a build of a Jenkins job, is it possible to change build parameters midway through?

Found the answer: use the EnvInject Plugin. One of the features is a build step that allows you to "inject" parameters into the build job from a settings file. I used one build step to create the settings file, then another build step to inject the new values. Then, all subsequent build steps and post-build operations used the new value.

Update with an example:

To add a new parameter (REPORT_FILE), based on existing one (JOB_NAME), inject a map with new or modified parameters in the Groovy Script box:

// Setting a map for new build parameters
def paramsMap = [:]

// Set REPORT_FILE based on JOB_NAME
def filename = JOB_NAME.replace(' ','_') + ".html"
paramsMap.put("REPORT_FILE", filename)

// Add or modify other parameters...

return paramsMap

Jenkins does have the ability to parameterize builds. For a string parameter, the developer can leave the field blank and then your build scripts can check to see if the env. variable for the parameter is set. If the env. var. is not set, the script can perform whatever calculation is needed (I don't think Jenkins has "pre-build steps") and pass it along. For a choice parameter the first line can be something like (Default), and again the build script can test its value and act accordingly.

Note on (Default)

I tried leaving the first line of the choice box blank, and Jenkins saved it correctly the first time; but when I came back to reconfigure the build Jenkins ran some kind of trim on options and the leading blank line was removed so I settled on (Default).

I hope this helps,
Zachary