Will Human expand further?

[The_Caveman]

The maps mark only the locations of systems that are:

A) known
B) inhabited
C) affiliated

There are plenty more systems in the IS other than the ones shown on the maps.

"Inhabited" is defined kind of loosely, too. Planets with extremely small populations, non-permanent habitation, etc. are left off the map unless they're otherwise notable. There are a lot of systems out there that have a few dozen people living in them, but they're not considered self-perpetuating colonies. Research outposts, mining expeditions, or just plain old hobo camps.
And then you have planets that were rendered post-apocalyptic wastes by the Succession Wars, that still have native populations but don't participate in the culture of the Inner Sphere at large. A few hundred or thousand survivors clinging to life in the ruins, with no access to space travel or communications. The planet itself is so badly damaged that it has no further value for scavengers, so no one goes there, so there's no point in showing it on the map.

[Maingunnery]

There are likely also many planets with sizeable populations that simply don't warrant including them because of a lack of usable infrastructure (as in pre-industrial).

[Col Toda]

There is no doubt many scattered colonies way beyond the periphery but how long or well they last without support from the inner sphere is the question . Most of ones that did likely have failed and only ruins are left . The Clans succeeded because they went out with tens of millions of people settled a couple of worlds and supported each other . The reason why people left would indicate how successful the colony would be . You would have religious groups who just want to be left alone and any number of political groups who are the losing side of a war which leave under equipped and likely to fail or ethnic groups who do not wish to become extinct in a modern society . I expect half die off completely and more than half of the remaining ones are in the process of dying off . Of the remaining one's many would be somewhat stagnant .  Just because of Murphy's law no more than a tiny percent would thrive .

[Maingunnery]

The Clans succeeded because they went out with tens of millions of people settled a couple of worlds and supported each other .

To be fair, the Clan Homeworlds are mostly crap, but they had enough resources and tech to adapt.

Groups with lesser tech/resources or preparation would need better worlds.

[Col Toda]

How good or bad a world ultimately is depends on how much the ecosphere lends itself to be terraformed and accept terrestrial plants and animals in which humans can eat .  The Biology on alien worlds would have a different lock and key protein system and would likely nothing would be eatable . Once you treat the soil and plant your terrestrial crops then you have to hope the indigenous diseases and molds do not adapt and kill off  your crops .  Things like hydroponics are less susceptible but it concentrates food production in a very vulnerable place for internal politics and external threats as all someone has to do to get power over the population is to take control of the hydroponic centers and all pirates would have to do is blast the food production and come back 2 years later and either blast it again or just loot the lifeless colony .  If food production is in the ground in too widespread and area then destroying that production becomes too resource intensive and you have to settle for raids or invasion . The Clans could have come across much nicer planets but moved on because of the indigenous plant and animal life or microbial conditions made it too labor intensive and risky to settle there .  The Clan Homeworlds were a cluster of usable worlds however less than ideal that did lend itself to colonization that were in close proximity from each other .  They settled there because it was good enough and morale was flagging in the search for a better situation . The colonization worked because they were close to each other and if any one of them came across a colony  extinction situation it could be averted by the support of the other worlds ; stand alone colonies die alone . The chances of absolutely nothing comes up that threatens or guarantees  colony failure  in the early decades would be slim to none . This is why though I think some widespread colonization has taken place they are scattered and few  surviving colonies far beyond the periphery and most of those just do not want contact with anything their ancestors fled to unknown space for .