With regards to Illinois Law, does it make any difference if the non-custodial parent paying child support is being sued for more

Child support is an on-going incremental obligation.  This requires payment in the ordered amount during the appropriate interval - weekly, bi-weekly, etc.  Modification can occur pursuant to a petition by either party to alter the support.  This can be a request to either increase or decrease support from the existing amount. While each case is determined by its own circumstances, statute does contemplate that the Courts can and will modify support.  In your situation, you should speak with an attorney as there may not be a sufficient factual and/or legal basis to increase support.  Simply because the statute provides a vehicle for the receiving parent to increase support does not automatically mean that such a motion will be granted. .