Using Acrobat Reader mobile app, you can Fill & Sign the document. However, to get other people to sign on it, you need to create a signature form field. Which isn't possible to do with freeware mobile app. For that you need Acrobat DC desktop app.
Can suggest an alternative for that. Open Document>Fill & Sign>at bottom menu-bar there's an option right after the dot and before oval shape, there's a line (-) option. Place that line on the form, where you want the other person to add their signature.
Send this form using share feature. End user will use the fill & Sign option to add signature on it.
This should fulfil your requirements without subscribing for a plan.