I don't have anything for this season, but the New York Yankees scored 152 runs in June of the 2024 season.

	TEAM	DATE	R	TM		OPP	RESULT	AB	H	2B	3B	HR	RBI	BB	HBP	SO	SB	CS	PA	TB	XBH	SH	SF	IBB	GIDP	AVG	OBP	SLG	OPS
1	Yankees	6/1/2024	7	NYY	@	SFG	W 7-3	34	11	1	2	2	7	1	0	9	0	0	36	22	5	0	1	1	3	.324	.333	.647	.980
2	Yankees	6/2/2024	7	NYY	@	SFG	W 7-5	38	11	2	1	2	7	5	0	12	2	0	43	21	5	0	0	0	0	.289	.372	.553	.925
3	Yankees	6/4/2024	5	NYY	vs	MIN	W 5-1	29	6	1	0	2	5	4	0	4	0	0	33	13	3	0	0	0	1	.207	.303	.448	.751
4	Yankees	6/5/2024	9	NYY	vs	MIN	W 9-5	31	9	2	2	0	9	6	0	11	0	0	38	15	4	0	1	0	0	.290	.395	.484	.879
5	Yankees	6/6/2024	8	NYY	vs	MIN	W 8-5	29	7	1	0	1	7	8	1	9	2	0	40	11	2	0	2	0	0	.241	.400	.379	.779
6	Yankees	6/7/2024	1	NYY	vs	LAD	L 1-2	38	5	1	0	0	1	3	0	12	0	0	41	6	1	0	0	0	1	.132	.195	.158	.353
7	Yankees	6/8/2024	3	NYY	vs	LAD	L 3-11	37	10	1	0	2	3	3	0	8	0	0	40	17	3	0	0	0	0	.270	.325	.459	.784
8	Yankees	6/9/2024	6	NYY	vs	LAD	W 6-4	31	9	2	0	3	6	2	0	14	0	1	33	20	5	0	0	0	1	.290	.333	.645	.978
9	Yankees	6/10/2024	4	NYY	@	KCR	W 4-2	31	9	0	0	0	4	1	2	6	0	1	37	9	0	3	0	0	1	.290	.353	.290	.643
10	Yankees	6/11/2024	10	NYY	@	KCR	W 10-1	38	10	0	1	3	10	3	1	8	0	0	42	21	4	0	0	0	1	.263	.333	.553	.886
11	Yankees	6/12/2024	11	NYY	@	KCR	W 11-5	36	11	0	0	3	11	4	1	5	1	0	42	20	3	0	1	0	1	.306	.381	.556	.937
12	Yankees	6/13/2024	3	NYY	@	KCR	L 3-4	31	5	1	0	1	3	2	0	8	0	0	33	9	2	0	0	0	1	.161	.212	.290	.502
13	Yankees	6/14/2024	8	NYY	@	BOS	W 8-1	37	10	3	0	2	7	4	0	11	2	0	41	19	5	0	0	0	1	.270	.341	.514	.855
14	Yankees	6/15/2024	4	NYY	@	BOS	L 4-8	34	6	0	0	1	4	6	0	10	0	0	40	9	1	0	0	0	0	.176	.300	.265	.565
15	Yankees	6/16/2024	3	NYY	@	BOS	L 3-9	33	6	0	0	2	2	2	0	14	0	0	35	12	2	0	0	0	1	.182	.229	.364	.592
16	Yankees	6/18/2024	4	NYY	vs	BAL	W 4-2	28	6	1	0	0	4	6	2	3	0	0	38	7	1	0	2	0	0	.214	.368	.250	.618
17	Yankees	6/19/2024	6	NYY	vs	BAL	L 6-7	34	9	1	0	1	6	9	0	5	0	1	45	13	2	0	2	0	2	.265	.400	.382	.782
18	Yankees	6/20/2024	5	NYY	vs	BAL	L 5-17	32	6	1	0	2	5	3	0	5	0	0	35	13	3	0	0	0	1	.188	.257	.406	.663
19	Yankees	6/21/2024	1	NYY	vs	ATL	L 1-8	27	3	0	1	0	1	3	0	12	0	1	30	5	1	0	0	0	2	.111	.200	.185	.385
20	Yankees	6/22/2024	8	NYY	vs	ATL	W 8-3	31	9	3	0	2	7	8	0	6	0	0	39	18	5	0	0	0	2	.290	.436	.581	1.017
21	Yankees	6/23/2024	1	NYY	vs	ATL	L 1-3	32	7	1	0	0	1	0	0	9	0	0	32	8	1	0	0	0	2	.219	.219	.250	.469
22	Yankees	6/25/2024	7	NYY	@	NYM	L 7-9	34	7	1	0	2	7	7	2	12	0	0	43	14	3	0	0	0	1	.206	.372	.412	.784
23	Yankees	6/26/2024	2	NYY	@	NYM	L 2-12	31	6	1	0	1	2	7	0	8	0	0	38	10	2	0	0	0	3	.194	.342	.323	.665
24	Yankees	6/27/2024	2	NYY	@	TOR	L 2-9	30	3	0	0	1	2	4	1	11	0	0	35	6	1	0	0	0	0	.100	.229	.200	.429
25	Yankees	6/28/2024	16	NYY	@	TOR	W 16-5	43	18	5	0	2	15	2	0	8	0	0	46	29	7	0	1	0	1	.419	.435	.674	1.109
	Total		152					902	219	36	7	37	147	110	11	242	7	6	1,036	380	80	3	10	2	26	.243	.329	.421	.750