There's "unknown" and there's "unknown." A 2009 paper ("HUMAN HEALTH RISK ASSESSMENT FOR ALUMINIUM, ALUMINIUM OXIDE, AND ALUMINIUM HYDROXIDE") states:

Aluminium hydroxide is one of the adjuvants most commonly used in routine human vaccines against hepatitis B virus (HBV), hepatitis A virus, and tetanus toxoid (TT) and in veterinary vaccines (see also Effects on Humans, Effects from Non-Occupational Exposure, Irritation, Irritation after Injection of Aluminium-Adsorbed Proteins (Vaccines and Hyposensitization Regimens)). Although it has been investigated since 1926, the mechanisms of action of aluminium adjuvants are not yet fully understood. It is likely that aluminium adjuvants induce immune activation which includes interleukin (IL) -1 production by monocytes, induction of eosinophilia, compliment activation and increased specific and non-specific immunoglobulin (Ig) G1 and IgE antibody responses (Gupta & Siber, 1995; HogenEsch, 2002; Jensen & Koch, 1988; Larsen et al., 2002; Norimatsu et al., 1995; Shi et al., 2001). Limitations of aluminium adjuvants for human vaccination include local reactions, augmentation of IgE antibody responses, ineffectiveness against some antigens and inability to augment cell-mediated immune responses, especially cytotoxic T-cell responses (Gupta, 1998).

Now, on to the question of "acceptable levels." Elsewhere in the same paper:

Further, the administration of aluminium-containing vaccines for extended time periods was found to be associated with the development of [macrophagic myofasciitis] at the injection site. In the past, individuals with impaired renal function receiving dialysis were reported to be at greater risk for aluminium intoxication associated with contaminated replacement fluids. However, this incidence has diminished markedly in recent years with the use of non-contaminated fluid and replacement of high-dose antacid therapy with alternatives. Although infants and children may be at higher risk for toxicity due to aluminium, a causal relationship was not confirmed. Hence, it should be noted that only at excessive concentrations of aluminium are toxic manifestations seen in human sensitive subpopulations.

I interpret this as saying that the reason there are "ZERO studies on acceptable levels of aluminum exposures" (and I have not researched this enough to be definitive that there are ZERO) is because there's no need to expose children to a high enough level of aluminum in order to find the limit. There's no major effect seen at current Al levels, other than reactions by a small population which has a reaction to the metal, and there are many cases where infants and young animals have been tested, without seeing obvious effects.

Indeed, there are plenty of papers which compare the effects of vaccines with and without aluminum adjuvants, in infants. One such is http://jid.oxfordjournals.org/content/184/9/1211.long . While http://www.biomedcentral.com/1471-2334/3/17/ doesn't compare the two but observes that "The 11-PncTD vaccine is safe, well-tolerated and immunogenic in infants."

So if the existing level of aluminum has an effect on infants then it's subtle. Now, do you really want people to put more aluminum into the bloodstream of infants in order to find out what the acceptable level might be? Or can we say that as best as we can tell, the current levels aren't a problem, and leave it at that?