This is a terrible idea for several other reasons than the good ones that T.M. mentioned.
For one thing the now modified home may command a much higher tax rate and when Mom dies it may be impossible to sell it. Suppose it's a 2000 sq ft home in a neighborhood of 2000 sq foot homes. You do this MIL apartment and now the taxing jurisdiction says "that's a duplex equivalent to 2 1000 sq foot homes your property tax just tripled" Then later on when you sell it even if the buyer rips out the modifications it will be a huge fight to get the tax rate dropped since the taxing authority is going to take the position that ANY remodels including ones to turn it "back" into a single family home increase value. You don't want to be the owner of the ONE house in the neighborhood that's assessed valuation is double every other home, you will never sell it.
Same goes for adding a floor if every other home is a single level and you have the only 2 story one it's going to be a lot harder to sell.
A second issue is that during the time Mom is still alive, the one family is going to be missing out on the equity gain of owning a home that they own outright. They may own a portion of Mom's home but since that's going to be split up when she dies they will only get 1/3 of the equity gain they would have got had they continued to own their own home.
Lastly, the facts of the matter are that in a great many cases, when someone gets older they start having medical issues. If Mom gets dementia 4 years from now and has to go into an assisted care facility then the entire equity of the home is going to go to pay for that and NONE of you kids will see a cent of inheritance. That will really financially screw over the family that moved into the house since they will have NO equity gain in that instance.
The reality is that you hit the nail on the head - Mom is lonely. The fact is that there is no moral responsibility for the children to provide for Mom's entertainment and trust me any of you who try doing this will come to regret it very quickly. In all likelihood unless Mom really loves living in the home for sentimental reasons or whatever, she would probably be just as happy selling it now and buying a condo then taking the extra money left over and rolling it into conservative investments like treasury bills or some such, then finding herself a boy toy and spending some of the extra money on cruises or some such. Then if she does get dementia then the money will be spent and she can just go into a Medicaid home which she won't care about, since she has dementia. Another option is a "retirement community"
Most grief counselors tell you to NOT make any major life changes for 1 year after a major life event such as the death of a spouse. You kids need to realize that this "scheme" is part of Mom's normal grieving process - people often like to jump into new and complex things (like a home remodel) as a way of distracting themselves from squarely dealing with their loss. Mom needs to come to terms with this and figure out her own life going forward and not try to permanently engage one of her kids and their families in this process. Also while you all may communally think this is a great idea I don't see you jumping in to volunteer to be the one, and I'd guess your siblings all privately are thinking that someone else in the family is going to be the one to do it. Unless one of the families is begging to be the one to move in, you are just all telling each other it's a great idea because none of you really know how to support your mother in her time of need.
Good luck on this, and definitely continue to talk privately with siblings WITHOUT mom being involved.