Overlap notes

First of all, English is not my first language so I'm sorry if my music vocabulary is a bit confusing, I'm not proficient with the English music language. Then, I'm having a bit of a problem trying to transcribe a piano sheet to Musescore. The reason I'm doing this is because the sheet is quite frankly illegible when printed so I need a cleaner version, but I can't quite transcribe it correctly because it has a lot of stuff like this:

You see, the dotted half-note at the beginning it's supposed to overlap with the eighth and quarter next to it, and extend until the quarter E note on the fourth beat of the measure. However, I can't put any of these E notes because if I put the dotted half-note at the beginning I can't write the eighth or dotted quarter and if I try to put these first and then the dotted half-note, it erases the other two. Same thing with the second half of the measure. Is there a way I can do this? Because there's got to be a way, right? Since this is pretty common on music sheet and this program has a lot of tools included. But I can't seem to find the way.

Thanks beforehand for your help and time and hopefully my wording on the music language wasn't too awful.