I would say that it is some sense obvious that higher intelligence is possible, because the process that led to whatever intelligence we have was haphazard (path-dependent, stochastic, and all that) and because what optimization did occur was under severe constraints - some of which no longer apply. Clearly, the best possible performance under severe constraints is inferior to the best possible with fewer constraints.

So, if C-sections allow baby heads to get bigger, or if calories are freely available today, changes in brain development that take advantage of those relaxed constraints ought to be feasible. In principle this does not have to result in people who are damaged or goofy, although they would not do well in ancestral environments. In practice, since we won't know what the hell we are doing... of course it will.

Still, that's too close to an existence proof: it doesn't really tell you how to do it.

You could probably get real improvements by mining existing genetic variation: look at individuals and groups with unusually high IQs, search for causal variants. Plomin and company haven't any real success ( in terms of QTLs that explain much of the variance) but for this purpose one doesn't care about variance explained, just effect size. A rare allele that does the job would be useful. I'd look at groups with high average IQ, but at others also.

There are other possible approaches. If you could error-correct the genome, fix all the mutational noise, you might see higher IQ. You could dig up Gauss and clone him. My favorite idea is finding two human ethnic groups that 'nick' - whose F1 offspring exhibit hybrid vigor.

As for the singularity: I could, I think, make a pretty good case that scientific and technological progress is slowing down.