§ IDefinition
ὑπεξαίρεσις — the "reserve clause," literally "a taking-out-from-under": the Stoic technical device by which a rational being sets out (TERMὁρμή) toward an external end, yet gives its assent conditionally — "if nothing prevents," "fate permitting." The impulse aims in earnest at the outcome, but the outcome is set in advance among the TERMpreferred indifferents (προηγμένον), not among goods; so failing to reach it does not shake one's inner evenness. The classical formula is μεθ' ὑπεξαιρέσεως ("with a reservation"): the wise man undertakes the deed while holding its result lightly.
The function of the reserve is to unite active engagement in the world with imperturbability. I am answerable for the right impulse and the TERMproper act, which are up to me, but not for the outcome, which is not up to me. Hence its linkage with the discipline of action (ὁρμή "with reserve") and the discipline of desire (acceptance of whatever outcome): a thwarted outward act does not thwart the inner disposition (διάθεσις) but is "turned about" (περιτροπή) — and the obstacle becomes material (05-20, 04-01).
§ IISource
The Stoic doctrine of "acting with reservation": Stob. Ecl. II.7 (the epitome of Arius Didymus — the doxography of the reserve); Sen. De tranquillitate animi 13.2–3 ("I will sail — unless something prevents; I will become praetor — unless something stands in the way"); De beneficiis 4.34.4 (the wise man is protected by the reserve clause (exceptio), "without which he decides on nothing and undertakes nothing"); Epict. Ench. 2 (desire and aversion, for now, only μεθ' ὑπεξαιρέσεως). The Latin calque is exceptio. In Marcus: 04-01 (Med. 4.1 — ὁρμᾷ πρὸς τὰ προηγούμενα μεθ' ὑπεξαιρέσεως); 05-20 (Med. 05-20 — διὰ τὴν ὑπεξαίρεσιν καὶ τὴν περιτροπήν); 06-50 (do the possible; if hindered, transfer to what is in your power, with reserve).
§ IIINotes
The reserve is not half-heartedness or slackness: I act at full strength but do not make the outcome a condition of my good. Its counterpart is περιτροπή ("turning-about"): together, in 05-20, they explain why an external hindrance does not touch the TERMimpulse (ὁρμή) or the disposition (διάθεσις) but only changes the material of action. The theological ground is that the outcome belongs to fate and providence: to "take it out" of one's claims is simply to acknowledge that it is not up to me. Thus ὑπεξαίρεσις is the precise operator that converts the pursuit of a TERMpreferred indifferent into a form compatible with imperturbability. See 04-01 (the image of fire that turns whatever falls in into fuel) and 05-20 ("the obstacle becomes the way").