Classical mereology is consistent with both the existence of gunk and either finite or infinite simples (see Hodges and Lewis 1968).
Of those philosophers who believe the material world contains simples, there has recently been debate over whether there can be extended simples (see Braddon-Mitchell and Miller 2006, Hudson 2006, Markosian 1998, 2004, McDaniel 2007a, 2007b, McKinnon 2003, Parsons 2000, Sider 2006, Simons 2004 inter alia).
Various reasons have been offered in favor of the claim that extended simples are possible, including: (a) that they are conceivable (Markosian 1998), (b) that purportedly plausible modal principles claiming, roughly, that there are no necessary connections between distinct existences entail their possibility (McDaniel 2007a, Saucedo 2009, Sider 2006), and (c) that contemporary physical theories entail that there are extended simples (Braddon-Mitchell and Miller 2006).
In the literature, however, the reasoning is often reversed: Those who think that extended simples are possible often use their purported possibility to argue against answers to the Simple Question that entail their impossibility and those who think that they are impossible uses their purported impossibility to argue against answers to the Simple Question that entail (or strongly suggest) their possibility.
Arguments include variants on Lewis' argument from temporary intrinsics, as well as arguments that intuitively an extended object must have, for instance, a right half and a left half, and thus have parts (cf Zimmerman 1996: 10) Similarly, one who endorses the Doctrine of Arbitrarily Undetatched Parts, which states that necessarily, if an object occupies region R then every occupiable proper sub-region of R is exactly occupied by a proper part of that object (see van Inwagen 1981), might use that principle in an argument against the possibility of extended simples.