Open access A la carte
Most of the major scientific publishers (Elsevier, Springer, Wiley, etc.) offer so-called "hybrid" journals: they are available only by subscription, but the author is free to publish his or her article open access, subject to payment of additional APCs.
Examples: Wiley OnlineOpen, Springer OpenChoice, Article Sponsorship (Elsevier) etc.
A costly open access option
Outside of negotiated agreements, the institution pays twice: once for the subscription to the journal, usually included in a package or collection, and once for the publication costs or APCs. The publisher, on the other hand, wins on both counts.
In addition, APCs are generally much higher for hybrid journals than for fully open access journals (average cost: €2500 for a hybrid journal versus €1500 for a fully open access journal*).
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* 2017 data from the national APC expenditure survey coordinated by the Couperin consortium and 2017 and 2018 data published on the OpenAPC platform by various institutions and consortia around the world.