Bearing in mind that no card other than "silver-bordered" cards has the same effect as that of Gleemax's ability:
If there is more than one instance of "You choose all targets for all spells and abilities" among permanents, their effects are applied in timestamp order, so that the controller of the permanent whose instance's effect has the latest timestamp among effects of those instances will "choose all targets for all spells and abilities" (C.R. 109.5, 613.10, 613.6; for this case in particular, see C.R. 613.6a, 613.6e). In general, this means the last Gleemax effect created "wins". See also this thread.
As an example, in general, if Mirage Mirror becomes a copy of Gleemax (and the two permanents are controlled by different players), Mirage Mirror's controller "choose(s) all targets for all spells and abilities", rather than any other player, at least until another Gleemax enters the battlefield or a permanent becomes a copy of an object that has Gleemax's ability.
If there is more than one instance of "You choose all targets for all spells and abilities" among permanents, their effects are applied in timestamp order, so that the controller of the permanent whose instance's effect has the latest timestamp among effects of those instances will "choose all targets for all spells and abilities" (C.R. 109.5, 613.10, 613.6; for this case in particular, see C.R. 613.6a, 613.6e). In general, this means the last Gleemax effect created "wins". See also this thread.
As an example, in general, if Mirage Mirror becomes a copy of Gleemax (and the two permanents are controlled by different players), Mirage Mirror's controller "choose(s) all targets for all spells and abilities", rather than any other player, at least until another Gleemax enters the battlefield or a permanent becomes a copy of an object that has Gleemax's ability.