This response is based on the information provided.  We suggest you discuss with your contracting and finance team, program manager and/or legal department as appropriate.

We are confused.  If the purchase has already been made "...use a BPA for purchase awarded to Dell...", then the question has been overtaken by events.

If the point is that Dell and the government have created a BPA and your team has been directed (mandated) to use the BPA, we offer the following.:

The BPA does not have automatic priority over pursuing small businesses.  BPAs are not mandatory sources as identified in FAR 8.002(a)(1).

If the order is under the SAT, then the FAR is direct that

FAR 8.004-Use of other sources, encourages the use of other non-mandatory sources which is where your BPS lies.  Yet it does not relieve you from considering small businesses.

"If an agency is unable to satisfy requirements for supplies and services from the mandatory sources listed in 8.002 and 8.003, agencies are encouraged to consider satisfying requirements from or through the non-mandatory sources listed in paragraph (a) of this section (not listed in any order of priority) before considering the non-mandatory source listed in paragraph (b) of this section. When satisfying requirements from non-mandatory sources, see 7.105(b) and part 19 regarding consideration of small business, veteran-owned small business, service-disabled veteran-owned small business, HUBZone small business, small disadvantaged business (including 8(a) participants), and women-owned small business concerns.

(a)(1) Supplies. Federal Supply Schedules, Governmentwide acquisition contracts, multi-agency contracts, and any other procurement instruments intended for use by multiple agencies, including blanket purchase agreements (BPAs) under Federal Supply Schedule contracts (e.g., Federal Strategic Sourcing Initiative (FSSI) agreements accessible at http://www.gsa.gov/fssi (see also 5.601)).....

....

(b) Commercial sources (including educational and non-profit institutions) in the open market."

However the DFARS leaves some room for the use of your vehicle.

"DFARS PGI 219.201  General policy.

      (c)(10)(2)  Modifications that increase the scope of the contract, or the order under a Federal Supply Schedule contract, should be reviewed by the small business specialist.  At a minimum, these actions might impact the small business subcontracting plan.  However, funding modifications or modifications that do not increase the scope of the contract generally should not be reviewed, because the value that a small business specialist review would add in these instances would be minimal compared to the resources that would be expended."

If your action is within the scope of the original BPA, not exceeding material, time or dollar thresholds, DFARS indicates using the BPA is a wiser allocation of the resources of the small business coordinator as well as the program office.