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.
The contract instrument you mention is an Indefinite-Delivery, Indefinite-Quantity contract (IDIQ). It is one of three Indefinite Delivery types of instruments - the other two being an Indefinite-Delivery, Definite Quantity (IDDQ) and a Requirements contract.
With an IDIQ, the Government's obligation is to the minimum quantity of supplies or services stated in the basic contract. In accordance with FAR 16.504(a)(1), the contractor must also furnish any additional quantities (over and above the stated minimums), NOT TO EXCEED THE STATED MAXIMUM in the contract. This "maximum quantity" (what you reference as the "ceiling") is further emphasized in FAR 52.216-22, a clause that is included in IDIQ contracts. In establishing this maximum quantity, the contracting officer should leverage market research, trends on recent contracts for similar supplies or services, poll potential users, or any other rational basis.
Both the solicitation and the contract are required to include the maximum quantity in accordance with FAR 16.504(a)(4)(ii)). Therefore, increasing it during the life of the contract to allow for additional task or delivery orders would likely result in a circumvention of full and open competition, and would require some sort of justification IAW FAR Subpart 6.3. In Liebert Corp., B-232234.5, Apr 29, 1991, the court rules that "An order in excess of the maximum quantity stated in the contract would be outside the scope of the contract. Such an order would result in a contract materially different from that for which the original competition was held and, absent a valid sole-source determination, would be subject to CICA requirements for competition."
Additionally, issuing a change order for such an action would not be allowed, as neither of the iterations of FAR 52.243-2 (the Changes clause for Cost-Reimbursement contracts) allow for changes to the maximum quantity.
Future IDIQs put in place for similar requirements should ensure the maximum quantity is arrived to after careful consideration of current circumstances.
In other words, this is an excellent "lessons learned" to apply in the future.