The following response is based solely on the question and background information provided. As we do not have all of the facts particular to your contract, program, and situation, we highly recommend you consult your Contracting Officer and Legal Office for guidance.
FAR 2.101 defines a couple of phrases that are important to this question. First, a "Classified Contract" means any "contract" in which the contractor or its employees must have access to classified information during contract performance. A contract may be a classified contract even though the contract document itself is unclassified. Then, a "contract" is also defined in FAR
Part 2, and includes such things as "orders". So, it's possible to have an order/contract that is classified without the base IDIQ itself being classified. It's a matter of access to the classified information during performance - in your case, performance that happens at the task order or delivery order level.
So, if the program or the IDIQ instrument itself is not classified, it does not necessarily prevent the Government from placing classified orders against it. This is especially true if the solicitation and resulting base contract(s) included a SOW/PWS that expressly states that the classification will be determined as orders are placed. With language such as that, and without further specificity within the solicitation, the contractor has some business decisions to make (do I even propose; if I do, what security requirements should I posture myself for; etc.). It was at this juncture that a protest based upon alleged apparent improprieties to the basic IDIQ solicitation could have been filed. Not doing so typically equates to the contractor surrendering to the risk involved.
A clause that was most likely included in your solicitation and resulting contract(s) is FAR 52.204-2. This clause points to the fact that it applies "to the extent that this contract involves" access to classified information. Naturally, this synchs with the prescription at FAR 4.404(a), where the clause is required in solicitation and contracts when the contract "may" require access to classified information. I only mention this initially because it supports that it is not unheard of to have certain aspects of a contract where the clause applies (classification exists), while there are others where it doesn't.
In cases where the totality of the orders placed against an IDIQ are classified, DFARS PGI 204.403 provides an actual template that Contracting Officers may use to specify the level of security clearance necessary to respond to the RFP. But, in your case where some orders are classified, while others are not, one could make the case that requiring a specific level of classification so that a contractor may simply be awarded an IDIQ might unduly limit competition. With such circumstances as yours, the contractor's aforementioned business decisions and the clause at 52.204-2 lay the foundation and mode of operation for subsequent orders that may be classified as "Confidential", "Secret" or "Top Secret". Specifically, paragraph "c" of the clause points to potential equitable adjustments due to changes to security requirements.
Finally, it will be the order awardee's contract file where the final 254 will reside. There is no reason to modify and include it within the contract file of the other IDIQ holders.