There are a number of ways to play as a construct or as a construct-controller.
Being a construct
The warforged race (Eberron Campaign Setting) is by-far the best way to play as a construct. There are a few other playable-by-the-rules construct races, but each penalizes you extremely hard for the privilege. The warforged get around this by limiting the benefits you get for being a construct via the Living Construct subtype. You can get most of those benefits back with the warforged juggernaut prestige class (Eberron Campaign Setting).
You can also be human and turn yourself into a construct, though the options for doing so permanently are both very poor. The green star adept (Complete Arcane) is actually one of the most notoriously-awful prestige classes in the game (pay a lot of gold for the “privilege” of losing five levels worth of spellcasting). The renegade mastermaker (Magic of Eberron) is less bad (and also super-cool), but it’s still basically ten levels (including two that miss out on spellcasting) for the effect of “being a warforged,” when, ya know, you could just start out as a warforged. In addition to these prestige classes, there are also a number of spells that can do it temporarily, such as body of war (Spell Compendium), though a lot of these are fairly high-level spells that turn around and prevent you from casting spells.
It actually gets you the elemental type rather than the construct type, but the elemental scion of Zilargo (Magic of Eberron) deserves mention just because it turns an elemental into a freaking Gundam mobile suit.
Controlling constructs can be simply a matter of taking the Craft Constructs feat as a spellcaster; artificers actually get the ability to craft homunculi (a certain class of construct) for free at fourth level, and also get numerous other item-creation bonus feats with which they can take the full Craft Construct. In addition to these, there is the effigy master (Complete Arcane), which makes specialized constructs known as effigies to do its bidding.
Warforged have items known as “warforged components.” Some of these simply slot into interfaces in their bodies, but others require some reconstruction to use. These seem quite perfect for you.
There are also construct graft options from Faiths of Eberron, which can attach warforged parts to creatures (including non-warforged), which also fits the bill.
Psychic warriors have numerous options for granting themselves natural weapons (powers like bite of the wolf, claws of the beast, etc.), or even grafting a manufactured weapon to their bodies (graft weapon power). And of course, druids and transmuters can change their bodies pretty easily, and along those lines the warshaper prestige class (Complete Warrior) can modify even just parts of its body. These could all be pretty easily fluffed as a construct that swaps out parts. Particularly the psychic warrior.
Being a construct
A synthesist summoner effectively “merges” his eidolon with himself; the eidolon can easily be described as a construct. The Advanced Race Guide also has rules for playing a half-construct. Additionally, wyrwoods (Bestiary 4) are presented as a character race, and manage to be true constructs rather than half-constructs of another type.
Controlling a construct
Craft Construct exists in Pathfinder as well as 3.5, so that is still an option. The summoner still works pretty well, this time without the synthesist archetype.
The summoner’s eidolon can vary quite a bit, which can easily be described as changing appendages. This seems like the best route to me. I’m not aware of anything equivalent to 3.5’s warforged components or construct grafting.
That said, Pathfinder has a lot of similar options for druids and transmuters as far as changing themselves go (and this is one place where Pathfinder has improved the game’s balance), and Dreamscarred Press has published a quite-well-made Pathfinder version of the psychic warrior.