Looking at the web site you linked, it appears that it is talking about various forms of individual saving, investment or pension plans. In other words, not really paying more to your state pension per se, but rather some kind of separate pension plan to supplement the public, government-funded pension.
That makes sense, too, given that many public pension schemes these days are centered around flows not funds. For public pension schemes, it's common for your tax money to go in and immediately back out, and in return, you get a promise that someone else's money will result in you receiving a certain pension payment later. (Sweden's current public pension scheme certainly works this way.) This stands in contrast to individual pension plans where the money you pay into the plan is earmarked for you specifically, and the less you pay or the worse your investment choices perform, the less you receive in payments in the end.
Especially under such an assumption, the question becomes: are you confident that future pensions will reflect today's promises, and are you happy with today's promises?
If the answer to either is any form of "no", then having some additional money somehow invested on the side makes sense. The amount would then depend on to what extent you distrust future pension payments. At one extreme we find full trust in the government's promises and no savings of your own; at the other extreme, you end up aiming for sufficient funds by retirement that you could live on those funds alone if necessary, treating the government pension plan as a bonus if it pays out as currently promised. Only you can know where on this continuum you stand, but I do recommend some soul-searching on the matter because the answer will hugely impact how much money you want to invest on the side.
Whether the amount is added to your government pension account or sits elsewhere (possibly locked away until you reach retirement age), if you plan to make additional payments to add to your later pension, you should make very, very certain that the money is booked to you specifically and cannot easily be transferred to other retirees by political decree. The easiest way to do that, if you have the self-discipline to not touch the money, is probably to open an individual investment account of some kind and contribute money to that.