For better or worse, I think JAS 39 Gripen was the last indigenous Swedish military jet we'll ever see. Now that we're in NATO there is no way you'll be able to convince the Swedish general public to pay up for another one.
In addition, if Gripen was expensive to research and design, imagine what the development costs would be for a new state-of-the-art multirole stealth fighter? Then split that on a production run of maybe max 200 aircraft for the SwAF. The only record that would break is the most expensive fighter per unit cost ever.
Then the alternative of doing it together with other EU countries? Maybe. But imagine getting France, Britain, Germany, Italy, Spain etc. (especially France

) sitting down at the same table to agree on what to build? And the result being something good and not another 2 kg Swiss Army knife (Panavia Tornado) you can't fit in your pocket?
No, I think we would be better off co-operating with the US and perhaps doing parts of whatever is in the pipeline. Something joint like the T-7A Red Hawk. But the US are big enough on their own so they would probably not think it worth the while. Doing something together with the British and/or Germans OTOH, that might work. But the whole EU? What could possibly go wrong......