Babe Ruth had the most games with 2+ home runs, with 72 games.

Interpreted as:

most regular-season games by a player with at least 2 hr under 44

	NAME	G	HR	AB	R	H	2B	3B	RBI	BB	HBP	SO	SB	CS	PA	TB	XBH	SH	SF	IBB	GIDP	AVG	OBP	SLG	OPS
1	Babe Ruth B. Ruth	72	146	298	177	183	13	4	278	46	0	26	1		345	642	163	1				.614	.666	2.154	2.820
2	Barry Bonds B. Bonds	71	146	280	167	182	8	0	243	41	2	26	10	2	324	628	154	0	1	11	3	.650	.694	2.243	2.937
3	Sammy Sosa S. Sosa	69	144	294	156	172	5	0	248	19	0	35	4	2	314	609	149	0	1	4	2	.585	.608	2.071	2.680
4	Mark McGwire M. McGwire	67	139	261	160	168	4	0	230	43	1	32	1	0	306	589	143	0	1	10	5	.644	.693	2.257	2.950
5	Albert Pujols A. Pujols	65	134	271	155	172	6	0	232	29	6	24	1	1	307	580	140	0	1	10	4	.635	.674	2.140	2.814
6	Willie Mays W. Mays	63	130	272	153	166	3	4	214	26	2	21	4	4	300	567	137	0	0	3	2	.610	.647	2.085	2.731
7	Alex Rodriguez A. Rodriguez	62	129	266	161	164	9	0	244	30	4	28	5	2	303	560	138	1	2	1	4	.617	.656	2.105	2.761
8	Hank Aaron H. Aaron	62	125	256	144	159	9	1	219	27	0	17	0	0	285	545	135	0	2	7	2	.621	.653	2.129	2.782
9	Ken Griffey Jr. K. Griffey Jr.	55	112	233	134	146	11	0	189	21	4	21	2	0	260	493	123	0	2	5	3	.627	.658	2.116	2.774
10	Jimmie Foxx J. Foxx	55	112	227	138	142	10	1	208	39	0	18	2		266	490	123	0			0	.626	.680	2.159	2.839
11	Manny Ramirez M. Ramirez	54	110	224	131	144	10	0	208	23	1	27	0	1	249	484	120	0	1	0	5	.643	.675	2.161	2.835
12	Frank Robinson F. Robinson	54	109	216	125	132	8	1	193	23	3	18	1	1	243	469	118	0	1	4	4	.611	.650	2.171	2.822
13	David Ortiz D. Ortiz	51	102	218	119	134	10	0	175	14	0	19	0	0	233	450	112	0	1	5	0	.615	.635	2.064	2.699
14	Carlos Delgado C. Delgado	49	104	208	120	122	8	1	188	20	4	25	0	0	236	444	113	0	4	6	1	.587	.619	2.135	2.753
15	Eddie Mathews E. Mathews	49	99	209	114	124	4	0	177	16	0	15	2	0	227	425	103	0	2	1	2	.593	.617	2.033	2.650
16	Mel Ott M. Ott	49	99	201	124	127	9	0	180	24	2	7	1		228	433	108	1			0	.632	.674	2.154	2.828
17	Jim Thome J. Thome	48	98	189	112	117	9	0	167	29	0	28	1	0	220	420	107	0	2	5	3	.619	.664	2.222	2.886
18	Juan Gonzalez J. Gonzalez	48	99	213	108	125	8	1	181	9	0	32	0	0	223	432	108	0	1	4	4	.587	.601	2.028	2.629
19	Harmon Killebrew H. Killebrew	46	93	181	99	107	2	0	157	19	3	18	0	1	203	388	95	0	0	1	0	.591	.635	2.144	2.779
20	Mickey Mantle M. Mantle	46	93	181	111	116	4	1	160	30	0	17	5	0	211	401	98	0	0	4	1	.641	.692	2.215	2.907
21	Mike Schmidt M. Schmidt	44	92	187	109	118	6	1	173	23	2	15	3	3	213	402	99	0	1	6	3	.631	.671	2.150	2.821
22	Willie McCovey W. McCovey	44	91	165	98	99	1	0	151	29	3	17	0	2	199	373	92	0	2	6	2	.600	.658	2.261	2.919
23	Manny Machado M. Machado	43	88	186	98	111	4	0	149	14	0	11	5	0	200	379	92	0	0	4	7	.597	.625	2.038	2.663
24	Miguel Cabrera M. Cabrera	43	88	182	106	125	10	0	151	14	1	13	0	0	198	399	98	0	1	5	3	.687	.707	2.192	2.899
25	Andruw Jones A. Jones	43	88	182	97	106	4	0	149	11	1	23	2	0	195	374	92	0	1	2	1	.582	.605	2.055	2.660