After showing all the restrictions, I will investigate the possibilities that still … for activism.
The verbs coming to my mind are hold and maintain. But I don’t know if these are good choices, and which one is better.
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"Maintain" is not proper. "Hold" would do depending on the context; if, for instance, you are considering a set of legal possibilities that result from a certain politics, and if in a particular case, certain legal restrictions are added to change these, then the nature of those resulting possibilities is compatible with the use of "hold".
(OED) be or remain valid, apply
If, instead, the possibilities are not the very articles of the law, but the particular activities that these laws take into account, "hold" is not a very good choice. In such a case a more precise verb would be "obtain".
(OALD) obtain 2 [intransitive] (not used in the progressive tenses) (of rules, systems, customs, etc.) to exist
(SOED) obtain 6 v.i. be prevalent, customary, or established; subsist, hold good,be in force or in vogue.
Note that this verb could also be used in the first context.