Could you achieve the same position you would have on a bigger frame by raising seatpost and stem? And how could I adjust those to "simulate" a bigger sized frame?
Any frame can support a range of rider sizes by adjusting (among other things) the seat post and stem. However, as you might suspect, there are compromises to be made. And, there are limits to how big of a rider can fit on a given frame. I'll explain a bit more below to illustrate these points.
You can adjust the seat post by making it higher (may require a longer seat post than you currently have). Also, some seat posts are straight, whereas others have a setback. The later will move the seat slightly further back on the bicycle. Setback is usually used to ensure that the rider is properly aligned over the pedals. Whereas height is used to ensure that the ride achieves a proper leg extension.
Next you will want to consider the distance from the saddle to the handlebars. The horizontal distance can be adjusted by getting a longer stem. And the vertical distance can be adjusted by getting a stem with a different rise (the angle of the stem relative to the front head tube). Therefore, you can achieve a wide range of positions.
However, thus far, we have basically ensured that the rider's legs are extending far enough and that his/her reach is correct. If that were the end of the story, then you'd be able to have a single size frame fit everyone by using a very wide range of stems and seat post sizes. Yet, if you shop the market, you'll find that each of these items tend some have a somewhat limited range of sizes available. The reason for this is that once you go beyond these limits, you start running into other issues. The rider's position begins to shift such that the center of gravity is too far in one direction. The steering becomes harder to manage. Or the drop (the vertical distance between the saddle and the handle bars) becomes too great making the bike uncomfortable to ride.
Tldr; For the best comfort and handling, stem and seat posts should be use to fine tune a bike's fit, rather than correcting for an otherwise improperly sized frame.
There isn't always one size frame which fits a person well in a given model line of bikes (there may be 2 or more - probably 2 if someones on the border of sizes). In some cases, you can get multiple models to fit by swapping out stems and seatposts and saddle and handlebar adjustments or swaps. However, this is highly dependent on the particular model of the bike and the rider.
The best solution for this sorta problem is to get a bike fit, which may show its not even possible. Otherwise, you have to just play with it on feel, which can get a bit expensive if you don't have all the parts on hand already. Pretty much all you can do though is put a longer stem, possibly raise and lower it, use wider handlebars and adjust the saddle angle+ position a bit further back (which may be easier with a different seat post).
The biggest things you have to do are get the effective top tube right. Then you have seat height and angle and handlebar height and stuff. Its not exactly a science though so you have to play around with it.