How to increase number of outliers in a dataset?

I'm assuming you want to create a point that, each column by itself appears normal, but when looking at all the columns appears as if it's an outlier (thus you'd need some sort of outlier detection). Thus the method of generating an outlier would require looking at all the dimensions in relation to each other. And since we didn't assume normality here, generating is not straightforward.

I would recommend first using some kind of outlier detection method from here on the original dataset, (Somethind like an Isolation Forest would work)

Then you can generate random numbers, (or use the numbers you generated) to test if they are outliers or not. This should be easy to do by hand since you only want 7 points and each point only has 4 dimensions. Also an additional tip would be to test the numbers using one of the methods that returns a score instead of a 0,1 prediction so that you can make sure it's not too obvious of an outlier (since you didn't want that).

Lastly, if you generated points, some sort of sanity check would be to append those points to the dataset, apply PCA to reduce the dimensions down to 2, plot the PCA result with a separate colour for the appended outlier points. And you can check by eye if the outliers are far apart but not too far apart from your dataset.

Hope this helps and gives you some ideas.