you can rebuild it w/polymer-modified cement resurfacing however you won't find anything acceptable at either an apron OR vest store,,, look for something at a pro const supply house,,, we do this work all the time using eliteCrete products.
Sika corp. makes all kinds of concrete patching products, I use them all the time.
Sika Top 122 plus is probably your best bet for this application if you just want to patch the stoop.
Sika has a training section on there web site.
well, there you have it - you asked repair & triumphant1 opines for replacement,,, obviously he sees sinking we don't,,, just repair it & don 't worry about the guy from gnu yawk :rofl:
pay attn 'cause i'm only going to say this once,,, if you don't know what you're talking about, its often best to keep quiet,,, its VERY doubtful those manufacturing, distributing, & selling repair cements would still be in biz IF the stuff didn't work,,, its accepted by DOT's everywhere incl nyc & nys,,, also very doubtful we'd still be using it after 39yrs if it didn't work !
There are good products available. Look up your local mason supply house or builders supply (not big box stores) and ask them what their customers (the pros -like 'itsreallyconc') use. Companies that do this work for a living have to stand behind their work. Use what they use.
To repair or replace -is always the question. Depends upon your needs and resources. Your photo doesn't show any great cracks. If true (can't see it that well) it'll be way cheaper to fix it up.
I had a set of concrete steps that were cracked and a couple chunks missing from the edge of a couple of the steps. I used a 1/4" masonry bit and drilled / placed a plastic wall anchor in a couple of places where the chunks were missing -then drove a two inch screw in each, leaving about 1-1/2" hanging out. Around those screws I built up the cement a little the first day. A couple days later I built it up some more and finished it off. It was still there when I moved out 10 years later -which is the mail point.
Cement All by Rapid Set will work just fine. Get a test kit to make sure your Ph is balanced and clean it well with a pressure washer. Then mix a little cement all still to build up the low areas. Finally do a flood coat over the whole thing and rub it out.When it dries you will have a uniform cement color.