I don't know exactly what you have, but I would not use real jasmine in a soap because it would be prohibitively expensive (at least a hundred dollars USD for enough for one batch of soap). You might have something that is quite diluted, hence the scent not being strong enough.
Another reason I would avoid it is because most floral essential oils will either accelerate badly or cause Soap On A Stick, i.e. it will seize instantly. And you don't know if the scent will stick after curing. Not such a big deal if you put it in M&P soap, but there are oils that don't even stick in M&P soap. Most essential oils don't last long in any kind of soap, even if they seem to initially.
What I would do, is find a synthetic one that has good reviews and use that. Make sure the people reviewing it say that it behaves in the kind of soap you want to make. Sometimes a fragrance oil (synthetic) that smells like the real deal will behave in soap whereas the real thing won't. Plus, synthetics are more likely to stick in the soap longer.
Regarding whether it's possible to extract it in essential oil form, I'm not sure. Only that it's normally sold as an absolute. It has to do with the extraction methods that are possible with a particular plant. For instance, I know that there's no such thing as vanilla EO, only an oleoresin can be extracted. But I'm not exactly sure of the reasons for this. It might be that the chemical components of the plant that contribute to the characteristic aroma of that plant have a heavier molecular weight and are not extractable by steam distillation. In other words, an EO extracted from the same plant would smell different than what you think of as "Jasmine". A good example is rose. If you compare rose otto and rose absolute, they smell different and yet are produced from two different ways of extracting oil from the same plant.
If you want to blend other floral EOs with jasmine to boost the scent, the only ones that come to mind are also super expensive and/or particularly troublesome in soap. That would be rose, and neroli.
